BCA - FCIT - Sem I

Theorems of Boolean Algebra Boolean Algebra
And Logic Gates
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NOTES
The following theorems are important to solve boolean expressions -
51
Theorem 1 :

A Boolean expression, in which the operations of + or. Operators have been performed
on a single Boolean quality, then its value is equal to the Boolean quality itself, i.e.
it remains unchanged.

If a ∈ S - a = a
a
a+a=a a
and a . a = a aa
Theorem 2 :

Indentity Law : =

If a ∈ S

a + 1 = 1 and 1 + a = 1

a . 0 = 0 and 0 . a = 0 a 1
Theorem 3 : ...... =
1
Absorption Law : =
a
If a, b ∈ S,

a + (a . b) = a
and a . (a + b) = a

Theorem 4 : aa
Complementation Law : 1=

If a ∈ S,

(i) (a')' = a aa a
(ii) 0' = 1 1b =
(iii) 1' = 0

DE MORGAN'S THEOREMS

De Morgan was a friend of George Boole who did research on logical mathematics. He
propounded two following theorems -

Theorem 5 : According to this theorem the value of the complement of the sum of
two boolean quantities is equal to the value of the product of separate
complements of these quantities.

(a + b)' = a' . b'

Theorem 6 : According to this theorem, the value of the complements of the products
of two boolean quantities is equal to the sum of separate complements
of these quantities."

(a . b)' = a' + b'

The following theorems are used to simplify the boolean expressions which also simplifies
the making of electronic circuits based on the expressions and their effect and action

Fundamentals of remain the same. For example, there is an expression a + (a . b). The circuit prepared
Computers & on its basis will be as follows-
Information Technology
a
NOTES ab

While, according to theorem-3, a + (a . b) = a, therefore the simplified expression of
a + (a . b) is a, therefore, the circuit prepared on the basis of expression a is as
follows -

a

The action and effect of both the circuits of the above given pictures are same, but the
circuit of the later picture is not more complex as compared the previous one. Therefore,
the circuit of the later figure is used.

Reducing Boolean Expressions by their Simplifications

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The boolean expression for an operation may be complex. These complex expressions are
simplified with the help of the postulates and theorems of boolean algebra. It has the
following examples -

Example 1 : Simplify -

a . (a + b)

Solution : a . (a + b) =a.a+a.b

= a + a . b (from theorem 1 a . a = a)

= a (from theorem 3, a + a . b = a)

therefore, a . (a + b) = a

Example 2 : Prove -

a + (b + b') + b = 1

Solution : L. H. S. = a + (b + b') + b

= a + 1 + b (from law 6 b + b' = 1)

= (a + 1) + b

= 1 + b (from theorem 2, a + 1 = 1)

= 1 (from theorem 2, 1 + b = 1)

= R. H. S. (proved).

Example 3 : Prove -

(a + b)' . b' = a' . b'

Solution : L. H. S. = (a + b)' . b'

= a' . b' . b' (from De Morgan (Theorem 5) theorem (a+b)' = a' . b')

= a' . (b' . b' )

= a' . b' (from theorem 1, a . a = a, so b' . b' = b')

52 = R. H. S. (proved).

Example 4 : Prove - Boolean Algebra
And Logic Gates
(a + a) . a. a + 1 . b = a + b
NOTES
Solution : L. H. S. = (a + a) . a . a + 1 . b
= a . a . a + 1 . b (theorem 1, a + a = a) 53
= a . (a . a) + 1 . b
= a . a + 1 . b (from theorem 1, a . a = a)
= a + 1.b (from theorem 1)
= a + b (from postulate 5, 1 . b = b)
= R. H. S. (proved)

Example : 5 Prove -

(a + b . c)' = a' . (b' + c')

Solution : L. H. S. = (a + b .c)'
= a' . (b . c) (from De-Morgan's theorem)
= a' . (b' + c') (from De Morgan theorem)
= R. H. S. (proved)

Example 6 : Prove -

a . (b.c) .c' =0

Solution : L. H. S. = a . (b . c) . c'
= a . b . c . c' (from postulate 4 a. (b.c)=a.b.c)
= a . b . (c . c')
= a . b . 0 (from postulate 6 c . c' = 0)
= a . (b . 0)
= a . 0 (from theorem 2, b . 0 = 0)
= 0 (from theorem 2, a . 0 = 0)
= R. H. S. (proved)

PROVING THE EQUATIONS OF BOOLEAN EXPRESSIONS BY TRUTH TABLE

The truth tables are used to certify the simplified form of complex boolean expressions.
In truth tables, columns are prepared for the LHS and RHS of the equation which is used
to express the simplified form of complex boolean expressions. After this, the equality of
LHS & RHS is checked for all the possible values (1 and 0) of boolean quantities If each
value is equal then, the equation is proved.

Example 7 : Prove the following equation with the help of a truth table :

(a + b)1 = a' . b'

Solution : For this equation we keep all possible values of two boolean variable
quantities and write the columns of the expressions of equations in the
following way-

L.H.S. R.H.S

a b a + b (a + b)' a' b' a'.b'
1010010
0110100
1110000
0001111

Fundamentals of In column 4 and column 7 the elements of each row are same,
Computers & therefore, (a + b)' = a' . b' is proved
Information Technology
L.H.S. R.H.S
NOTES
ab c b.c (a+b.c) (a+b.c)' a' b' c' b'+c' a'.(b'+c)'
54 00
00 00 0 1 111 1 1
01
01 10 0 1 110 1 1
10
10 00 0 1 101 1 1
11
11 11 1 0 100 0 0

00 1 0 011 1 0

10 1 0 010 1 0

00 1 0 001 1 0

11 1 0 000 0 0

Example 8 : Prove the following equation with the help of truth table :
Solution : (a + b.c)' = a' . (b' + c')
Example 9 :
Solution : Here, there are equal elements in the rows of column 6 and column 11,
therefore, (a + b .c)' = a' . (b' + c') is proved
Solve the following equation with the help of truth table -

(a')' + (b')' = a + b

a b a' b' (a')' L.H.S. R.H.S
(b')' (a') + (b')' a+b
0 0 11 0 00
11 0
0 1 10 0 01 1
11 1
1 0 01 1 1

1 1 00 1

In the above truth table, the elements of column 7 and column 8 are
same. Therefore (a')' + (b') = a+b is proved.

PRINCIPLE OF DUALITY

Boolean postulates menage the operations of the operators AND and OR, 0 and 1. There
is dual recognition of boolean expressions, which is called duality. It can be obtained the
following way :

l Replacing the . sign with +

l Replacing the + sign with .

l Separating all NOT operators.

For example : The boolean expression a + a' = 1 can be turned into dual boolean
expression a . a' = 0 by following the abovesaid 3 steps.

Likewise dual boolean expression a . (a + b) = a can be turned into a + (a . b) = a.

The dual theorem table of some theorems has been displayed below : Boolean Algebra
And Logic Gates
Theorem Dual theorem
NOTES
a+0=a a.1 = a
a + a' = 1 a. a' = 0 Check Your Progress :
a+a=a a.a=a 1. Define Boolean Algebra ?
a.1=1 a.0=a 2. What do you mean by truth
a + a.b = a a.(a+b) = a
(a')' = a (a')' = a table.
a.(b+c) = a.b + a.c a + (b.c) = (a+b) . (a+c) 3. What is sum of product ?
a + a'.b = a + b a . (a' + b) = a . b 4. What is product of sum ?
(a + b)' = a' . b' (a . b)' = a' + b'
55
Table 3.6

Standard Forms

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A boolean expression can be defined by the following conditions -

n Product : In this condition, one or more boolean variables are Logic gate
added by AND operator. For example : a . b . c is a product processes signals
condition.
which denote
n Sum : In this condition, one or more boolean variables are true or false.
added by OR operator. For example : a+b+c is a sum
condition.

n Sum of Products : It is such a boolean expression whose product conditions are
connected/added by OR operator. For example : a'c + bc' is the sum of products.

n Product of Sums : It is such a boolean expression whose sum conditions are co-
ordinated by AND operator, for example : (a+c).(b+c) is a product of sums.

Basic Logic Gates

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Let's start this section with the question 'What is a logic gate ?' this question initiates this
section. In digital computers, all the operations are carried out through signals. These
signals are obtained from the standard blocks of the internal circuit of the computers.
These circuits are called logic gates. If we have to define it in one sentence then, the logic
gates are the base of electronic circuits of the computer.

AND Gate

AND Gate has a digital circuit, which has one or more inputs and only one output. In
the AND gate displayed in the picture below, a and b are inputs and c is output. In
this gate, if the values of inputs a and b we true, the output will be true. The truth
table of this gate will be as table 3.7.

a a b c = a.b

c=a.b 00 0

b 01 0

10 0

11 1

Fig. 3.7 : AND Gate Table 3.7 : AND Truth Table

Fundamentals of OR Gate
Computers &
Information Technology OR gate is a digital circuit which has one or more inputs and only one output. In
the OR gate displayed in the following picture, a and b are inputs, while c is the
NOTES output. In this gate, if the value of input a or input b is true, the value of output
c is true. The truth table of this gate will be as follows :
56
a a b c = a+b

c=a+b 00 0

b 01 1
10 1

11 1

Fig. 3.8 : OR Gate Table 3.8 : OR Truth Table

NOT Gate

NOT gate is a digital circuit which has one input and only one output. In the NOT
gate displayed in the following picture, a is input while c is the output. In this gate,
the complement a' of input a is obtained as output. Therefore if the value of input
a is true the value of output c will be false. The Truth table of NOT gate will be as
follows :

a c = a' a c = a'

Fig. 3.9 : NOT Gate 01
10

Table 3.9 : Truth table for NOT Gate

NAND Gate

NAND gate is the combination a C = (a . b)1
of AND and NOT gate is which
the output of AND gate is

inverted by NOT gate. NAND

gate is expressed through figure b

3.10, while its symbolic

sepresentation is expressed by Fig. 3.10 : The circuit of NAND Gate

figure 3.11.

a
C

b

Fig. 3.11 : The symbol of NAND Gate

The truth table of NAND gate will be as follows :

a b c = (a.b)'

00 1
01 1
10 1
11 0

Table 3.10 : The truth table of NAND Gate

NOR Gate a C = (a + b)1 Boolean Algebra
b And Logic Gates
It is a set of OR gate and NOT
gate in which the output of OR Fig. 3.12 : The circuit of NOR GAte NOTES
Gate is inverted by NOT gate.
The circuit of NOR Gate is C 57
expressed by figure 3.12 while
its symbolic representation is
expressed in figure 3.13 :

a

b

Fig. 3.13 : The symbol of NOR Gate

The truth table of NOR Gate is as ofllows :

a b c = (a+b)'

00 1
01 0
10 0
11 0

Table 3.11 : The truth table of NOR Gate

XOR Gate (Exclusive OR Gate)

It is a combination of AND, NOR and OR gate in which both outputs obtained from
AND gate and NOR gate are inputs in OR gate and from this OR gate, the output
of the entire combination is obtained.

If any one input is True in this gate then the output is true, but if both the inputs
are true, the output is false.

The circuit of XOR Gate is expressed in figure 3.12, while its symbolic representation
has been expressed in figure 3.13.

To express operations on boolean variables of XOR gate the ⊕ sign is used. The truth

table of XOR gate is as follows :

a

b
C=(a + b)

Fig. 3.12 : XOR circuit

a
c

b

Fig. 3.13 : XOR Gate Symbol

Fundamentals of a b c = a+b
Computers &
Information Technology 00 0
01 1
NOTES 10 1
11 0

Table 3.12 : The truth table of XOR Gate

XNOR Gate (Exclusive NOR Gate)

XNOR gate is the inverse of XOR gate. In which there is a combination of a AND
gate and two NOR gates. Output of AND and one NOR one NOR gate are inputs
for the other NOR Gate and from it the output of entire combination is obtained. If
only one input from this gate is true then the output is fales but if both the conditions
of both the inputs are true or false, the output is true. The circuit of XNOR Gate has
been displayed in figure 3.14, while figure 3.15 shows its symbolic representation.

a

b
C=(a + b)
Output

Fig. 3.14 : The circuit of XNOR Gate

Fig. 3.15 : XNOR Gate symbol

The truth table of XNOR Gate is an follows :

a b c = (a ⊕ b)

00 1
01 0
10 0
11 1

Table 3.13 : The truth table of XNOR Gate

Use of Logic Gates in Circuits

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We know that circuits are prepared on the basis of boolean algebra and its expressions.
Logic gates are used to create circuit diagrams by applying them in place of boolean
operators (such as- OR, AND, NOT etc.) applied in boolean expressions.

58

Example 10 : There is a boolean expression as follows. Prepare a circuit for it. Boolean Algebra
And Logic Gates
p = ab' + ab + b
NOTES
Solution : It circuit will be as follows :
59
a p=ab' + ab+b
b

a
b
b

Fig. 5.16 : The circuit prepared as per example 10.

Here if we simplify boolean expressions with postulates and theorems of boolean
algebra, a simpler but equivalent circuit may be created.

ê p = a.b' + a.b + b
ê p = a(b' + b) + b
ê p = a.1+b

= a+b

ê p = a + b (is a simplified expression)

Now we can prepare the circuit of the simplified expression a + b as per picture
3.17.

p=a + b

Fig. 3.17 : A circuit based on or simplified expression

Karnaugh Map

______________________________________________________________________K_a_r_n_a_u_g_h__M__a_p__is__

We know that algebric simplification is an art in which expanded and also called Veitch
complex circuits are simplified and shortened. But if the number of diagram

expressions is more, this method may prove erroneous, therefore so

many engineers don' use algebraic simplification method.

Karnaugh Map is a popular way of simplifying boolean expressions. This is a method to
present the truth table in a pictorial way. It was developed by Maurice Karnaugh in Bell

Fundamentals of Laboratories. In this method, the truth table is divided into rows and columns in
Computers &
Information Technology sequares and in the squares related to the row number. Every digit of minterm 1 of

NOTES a truth table is placed in the related square related row1. In the following picture a

60 karnaugh map for one variable has been displayed. We see in this figure that there

are two squares in it, which have been given numbers 0 and 1 in which 0 stands for

row 0 of the truth table and 1 refers to the row 1 of truth table. Now, let us consider

the following truth table for variable A and output y. 0 1

Ay A

01

1 0 = Σ0 Fig. 3.18 : Karnaugh Map for

one variable

The above truth table can be expressed by Σ 0 in AND-OR condition. Here in the truth

table, the row 0 is a Minterm. Now for the row related to 0 a 1 will be placed in the
square 0 of Karnaugh Map which will provide the following map.

01

A1

Thus for the truth table for one variable a karnaugh map is prepared. Karnaugh. Maps for
2, 3 are 4 variables are displayed in figures 3.19, 3.20 & 3.21 respectively. It should be
noted that the number of squares are in no way related to the binary digits in the Map.
If they are converted from complement to uncomplement, the order of deciding the digits
will be 00, 01, 11 and 10.

B 0 1 BC
A A 00 01 11 10

0 0

11

Fig. 3.19 : Map of 2 variables Fig. 3.20 : Map of 3 variables

CD
AB 00 01 11 10

00 B
01
11
10

Fig. 3.21 : Map of 4 variables

In this indication of map, '1' indicates that the status of the concerned variable is in the
left corner of the map and it is true, while a '0' means the condition of variable is false.
For example, in the first figure the meanings of variables B and C : 00, 01, 11, 10 are
B'C', B'C, BC and BC' respectively.

Summary Boolean Algebra
And Logic Gates
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NOTES
l Boolean algebra is the algebraic structure of abstract algebra which discusses
essential properties of set operations and logic operations. Check Your Progress :
5. What do you know about or
l Boolean Algebra, a branch of Algebra was invented by a British Mathematician
George Boole (1815-1864). Gate ?
6. Write the truth table for
l Boolean Algebra is used to simplify Electonic Digital Circuits.
XNoR Gate.
l According to Boolean Algebra, there are two possibilities for a statement. 7. What is KMap ?

l These complex circuits are expressed in the statements of boolean algebra and are 61
simplified using the postulates of Boolean Algebra.

l When two statements are combined to form a new statement, this new statement
is called compound statement.

l A table which expresses all the possibilities of a switching circuit in the form of
binary valued quantity 1 and 0 is called Truth Table.

l In Boolean Algebra to simplify the complex expression there are some accepted
facts and postulates which are the foundation of boolean algebra.

l De-Morgan was a friend to George Boole who researched on Logical Mathematics.

l According to theorem 5 of De-Morgan the value of the complement of the sum
of two boolean quantities is equal to the sum of semparate complements of these
quantities.

l According to De-Morgan's theorem 6 the value of the complement of the products
of two quantities is equal to the sum of the complements of these quantities
taken separately.

l To certify simplified forms of complex boolean expressions, truth tables are used.

l Boolean postulates operator AND and OR plan the operations of 0 and 1. In it
there is dual identity of boolean expressions which is called duality.

l AND gate is a digital circuit (dual state) which was more than one inputs and only one
output.

l OR gate is a digital circuit which has more than one inputs and only one output.

l NOT gate is a digital circuit which has one input and one output.

l NAND gate is a combination of AND and NOT gate, in which the output of AND
gate is inverted by NOT gate.

l NOR Gate is a set of OR gate and NOT gate in which the output of OR gate
is inverted by NOT gate.

l XOR gate is a combination of AND, NOR and OR gates in which both the outputs
obtained from AND gate and NOR gate are input in the OR gate and this OR
gate gives the output of the entire combination. Any one input being true in this
gate, the output is true, but if both the inputs are true, the output is false.

l XNOR gate is the inverse of XOR gate. It is a combination of one AND gate and
two NOR gates. The outputs obtained from its AND gate and NOR gate are input
in another NOR gate and it gives the output of the entire combination. Any one
input being true in this gate, the output is false but if both the conditions of both
inputs are true, the output is true.

l Karnaugh Map is a popular method of simplifying boolean expressions. This is
mode of presenting the truth table in the form of a picture. This technique was
developed by a telecommunication engineer Moris Karnaugh in the Bell laboratories.

Answer of the Check your progress :

1. Introduction–Boolean Algebra is the algebraic structure of Abstract Algebra in which
required properties of set operations and logic operations. Expecially it contains intersec-
tion, union and complement set operations and AND,OR and NOT logic operations.
Logic gates act on signals which express true or false. Logic gates help in building a circuit.

2. Truth table is a kind of mathematical table which is used to determine whether an
expression is true or false in the logic.

Fundamentals of 3. Sum of Products–It is such a boolean expression whose product conditions are con-
Computers & nected/added by OR operator. For example : a'c + bc' is the sum of products.
Information Technology
4. Product of Sums–It is such a boolean expression whose sum conditions are co-ordinated
NOTES by AND operator, for example : (a+c).(b+c) is a product of sums.

62 5. OR gate is a digital circuit which has one or more inputs and only one output. In the
OR gate displayed in the following picture, a and b are inputs, while c is the output.
In this gate, if the value of input a or input b is true, the value of output c is true.

6. The truth table of XNOR Gate is an follows :

a b c = (a ¿ b)

00 1

01 0

10 0

11 1

7. Karnaugh Map is a popular method of simplifying boolean expressions. This is mode of
presenting the truth table in the form of a picture. This technique was developed by a
telecommunication engineer Moris Karnaugh in the Bell laboratories.

Exercise

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1. Boolean Algebra was named after which mathematician ?
2. Explain Boolean Algebra in your own words ?
3. What are the main principles of Boolean Algebra ?
4. Define switch and switch circuit.
5. What is truth table ?
6. What do you mean by compound statement ?
7. What are the postulates of Huntington ?
8. Explain the postulates of Boolean Algebra.
9. Explain various theorems of Boolean Algebra.
10. Explain the theorems of De-Morgan.
11. Prove the following :

(i) a + (b + b') + b = 1
(ii) (a +b)'-b' = a'.b'
(iii) (a+a).a.a + 1.b = a+5
(iv) a.(b.c).c' = 0
(v) (a+b.c)' = a'.(b' + c')
12. Prove (a+b)' = a'+b' with the help of a truth table.
13. What is the principle of duality ? Explain.
14. What do you mean by Logic Gates ?
15. Explain the following Gates :
(i) AND
(ii) OR
(iii) NAND
(iv) NOR
(v) XOR
(vi) XNOR
16. Prepare the electronic circuit of P = ab' + ab + b.
17. Explain the Karnaugh's Map.

4 Number System Number System
NOTES
The Chapter Covers :

n Introduction
n Digital and Analog Operations
n Binary Data
n Binary Number System
n Decimal Number System
n Octal Number System
n Hexadecimal Number System
n Fractional Conversion
n Coding System
n Summary
n Exercise

Introduction

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Computer does not understand our instructions directly, neither do we have the ability to
understand the basic instructions of the compuer. Computer undersands only 0 and 1 and
all our commands convert into these two digits with the help of translator program. Again
when we need the instructions of the computer, the translator program converts it into
the language understandable on the level of the user. This process can be understood
through various number system conversions explained in this chapter.

63

Fundamentals of Digital and Analog Operations
Computers &
Information Technology ______________________________________________________________________________________

NOTES Let's see what are digital and analog operations. In computer field, all the operations
performed by computers around us are digital. In addition, whenever we talk about a
computer, we mean digital computer. The operations based on numbers are called digital
operations. Therefore all the operations of digital computers depend upon number system.
Digital computers divide information in small pieces and use digits to express those pieces.
Digital computers complete the operations in the correct order of the terms. Every unit
of information is processed as per the different instructions.

Analog operations are those which don't use digits at all, but present data in alterable
points with a continuous spectrum of pre-defined values. To understand digital and analog
operations, two clocks have been shown below. The left clock shows the time in digits,
while the right clock has some values pre-marked and the hands of the clock show the
time with-respect to those pre-marked values.

Fig. 4.1 : Digital and Analog Operations through two clocks

Earlier, the computers were analog and most machines worked on the analog systems.
Thermometer is a device to measure temperature, is a common example of analog
operations.

Analog computer works in a way quite different from that of digital computer. Though
analog operations in some respects, are more flexible than digital operations, but the digital
operations are clearer and more reliable. Earlier, analog computers were meachanical with
tons of weight having several motors and gears to make calculations.

Binary Data

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Let us see, in this section, what binary data is computer, as we know, understands only
digits and in these only 0 and 1. 0 and 1 stand for two conditions. In fact, computers
represent data on the basis of the condition of the electronic switch. Switch, as we use the
bulb, has two conditions in it. The moment you put the switch on, the bulb is on, the
moment you switch it off, it gets off. Likewise, even computers have switches which
express the probable conditions on and off. When the switch is off in computes, if
expresses 0 and when the switch is on it represents 1. See figure 4.2, given below. that's
why it is said that 2 is the base on which the computer works, and it is called binary.

64

Fig. 4.2 : Binary states

0 and 1 are called binary digits. Binary digit is called bit in short. 4 bits make a nibble Number System
and eight bits make a byte. One byte denotes one character or space in a computer. NOTES
More than one bytes create one word. For example, COMPUTER is a word of eight
bytes and it can be expressed in binary as in figure 4.3 : 65

C 0100 0011
O 0100 1111
M 0100 1101
P 0101 0000
U 0101 0101
T 0101 0100
E 0100 0101
R 0101 0010

Fig. 4.3 : Binary conversion of the word COMPUTER

Binary Number System

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In the last section, you came to know what Binary Data is. Let us now find out what
is binary number system. In binary number system, there are two digits 0 and 1. That's
why the base of this number system is 2. In binary number system, the digits 0 and
1 are called Binary Digits or bits. The value of a binary number is found on the basis
of its place value in the order from right to left. For example, 110011 will have its
place value, as shown below :

1 100 11

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

This place value becomes the base for binary-decimal change, To express the base,
which has been displayed in the section given ahead. while displaying number,
the number enclosed
DECIMAL NUMBER SYSTEM within brackets and the
base is sub-scripted at
Now, we'll know what decimal number system is. In the bottom-right corner,
decimal number system there are 10 digits from 0 to 9. It so that we can know
has the base 10, as it has 10 symbols or digits. The value about the base to which
of any number written in decimal number-system has two the number belongs.
properties or meanings :

l Symbol Value : These are the digits from 0 to 9.

l Positional Value : The right to left direction of the number, in the order of
the power of base 10- such as thousand, hundredth. Tenth, unit etc. increases.

These are arranged as follows :

thousands ← hundred ← tenth ← unit The value of a num-
ber with power 0 is
The position of the negative digits goes from right to left and 1. Therefore 100 = 1.
starts from 0.

Such as .......... ← 3 ← 2 ← 1 ← 0

The place value of each digit is found by putting the power of the number of the

Fundamentals of position of that digit on its base and the value of that digit is equal ot the product of
Computers & the digit and its place value. The value of a given number is equal to the sum of the
Information Technology values of its digits.

NOTES For example : Decimal number 365 means :

66 Number digit value Position of Position The value of
digits right value the digits of
decimal number
to left

36 5

5 0 100 = 1 5x1 = 5
6 1 101 = 10 6x10 =60
3 2 102 =100 3x100=300
Sum = 365

Binary - Decimal Conversion

We have seen what binary and decimal number systems are. In this section we'll see how
to convert the binary number into decimal number system. To convert binary number into
decimal number each digit of binary is multiplied with its position value and the sum of
products is found. This sum of products is the equivalent decimal number to that binary
number.

Example 1 : Convert the binary number 1011001 into decimal number

1011001 22 = 4 21 = 2 20 = 1
0 0 1
26 = 64 25 = 32 24 = 16 23 = 8
1 0 11

1x 1= 1
0x 2= 0
0x 4= 0
1x 8= 8
1 x 16 = 16
0 x 32 = 0
1 x 64 = 64

89

10 1 1 0 0 1

64 32 16 8 4 2 1

64 + 0 + 16 + 8 + 0 + 0 + 1

= 89

therefore (1011001)2 = (89)10

Decimal - Binary Conversion

______________________________________________________________________________________

You have already learnt how to convert a binary number into decimal number. In this
section, you will understand, how is a decimal number converted into a binary number.
To convert a decimal number into a binary number the base 2 of binary number system
is used. Following are steps for it :

ê The given decimal number is divided by base 2 of binary number system.

ê The quotient is written under the number and remainder is written to the right.

ê The quotient obtained in step (2) is again dividec by 2 and the new quotient is Number System
NOTES
written below the quotient obtained in step 2 and to the right of the remainder.
67
ê Likewise, the process from step 1 to 3 is repeated until the value of quotient is

0.

ê The remainders of 1 and 0 is written from bottom to top order. The collected

remainder is the equivalent binary converted number of the given decimal number.

Example : Convert decimal number 89 into a binary number.

Solution : 2 89 remainder

2 44 1

2 22 0

2 11 0

25 1

22 1

21 0

01

therefore (89)10 = (1011001)2 Ans.
Example : Convert decimal number 52 into binary number.

Solution : 2 52 remainder

2 26 0

2 13 0

26 1

23 0

21 1

01

Therefore (52)10 = (110100)2 Ans.
Example : Find the equivalent converted number of decimal number 101.

Solution : 2 101 remainder

2 50 1

2 25 0

2 12 1

26 0

23 0

21 1

01

Therefore (101)10 = (1100101)2 Ans.

Octal Number System

______________________________________________________________________________________

In the previous section, you learnt about decimal number system. In this section you will
know about octal number system. There are eight digits (0, 1, 2, 3, 4, 5, 6, 7) in the Octal
Number System. Hence its base is 8. The positional value of each digit of an octal number

..... 84 83 82 81 80

4096 512 64 8 1

Fundamentals of Binary number can be understood through computer very easily. But big binary
Computers & numbers posed problems before the programmers. Therefore, they found a solution
Information Technology in which the set of three digits of a binary number can be expressed by one unit. One
digit of octal number system (0 to 7) represents the set of three binary digits. The digits
NOTES are grouped from right to left. (See the table).

68 Many computer manufactures use octal number system in computer hardware and
software.

Octal - Decimal Conversion

______________________________________________________________________________________

Let us try to know which steps are used convert octal into decimal. They are as follows.

ê Every digit of octal number is multiplied with its position value.

ê Thenafter, all the products are added. The sum obtained is its decimal equivalent.

For example (1501)8 is an octal number which is to be converted into decimal.
It will be done as follows :

1 5 01

↓ ↓ ↓↓

Positional value 3 2 10

Finding the power of ↓ ↓ ↓ ↓
positional value with 8
83 82 81 80

The products of its digits ↓ ↓ ↓ ↓
with their positional value
83 × 1 82 × 5 81 × 0 80 × 1

↓ ↓ ↓ ↓

512 × 2 64 × 5 8×0 1×1
= 1024 + 320 + 8 + 0
= 1345

Example : Find the decimal converted number of octal number 1204.

Solution : (83 × 1) + (82 × 2) + (81 × 0) + (80 × 4)

(512 × 1) + (64 × 2) + (8 × 0) + (1 × 4)

= 512 + 128 + 0 + 4

= 644

Therefore (1204)8 = (644)10 Ans.

Example : Find the decimal converted number of octal number (644)8.

Solution : (82 × 6) + (81 × 4) + (80 × 4)

(64 × 6) + (8 × 4) + (1 × 4)

= 384 + 32 + 4

= 420

Therefore (644)8 = (420)10 Ans.

Decimal - Octal Conversion Number System
NOTES
______________________________________________________________________________________

Let us see what steps are used to convert decimal to octal. To convert a decimal number
to octal, we devide the decimal number with the base 8 of the octal number and write
the remainders from bottom to top (vertical) order through the following steps :

ê The given decimal number is divided by 8, which is the base of octal number

system.

ê The quotient is written below the number and the remainder is written to its

right.

Quotients

(725)8

ê By again dividing the found quotient by 8, we write the new quotient below

the last quotient and the remainder to the right of it.

ê Similarly, keep repeating above three steps till the value of the quotient is 0.

ê Now the obtained remainders (0 to 7) are written vertically from bottom to

top. The same collected remainder is the octal-converted number of the given
decimal number.

In the following examples, we will discuss decimal-octal conversion.

Example : Convert the decimal number (420)10 into octal number. Check Your Progress :
1. What do you understand by
Solution : 8 420 remainder
analog & digital operations.
8 52 4 2. What is symbol value and
864
positional value.
06 3. Convert into decimal

Therefore (420)10 = (644)8 Ans. number from octal number
1204.

69

Fundamentals of Example : Convert decimal number (2967)10 into octal number.
Computers &
Information Technology Solution : 8 2967 remainder

NOTES 8 370 7
8 46 2
70 856

05

Therefore (2967)10 = (5627)8 Ans.

Binary - Octal Conversion

______________________________________________________________________________________

We'll know in this section how the binary-octal conversion takes place. From the left of
the binary number given for conversion from binary number to octal number, the sets of
binary numbers of three digits each are made. If there are less than three digits in the last
set (the left most) we ourselves put 0 to make it 3. Now, we write the octal number (given
in table 4.1) for each set. The value obtained is the converted octal number.

Binary Octal

000 0

001 1

010 2

011 3

100 4

101 5

110 6

111 7

Table 4-1 : Binary octal equivalent digits

Example : Convert the binary number (1101100012) into octal number.

Solution : First the number is divided in the sets of three digits in such a way, that there
will be only one binary digit left for the left most set. we put two zeros from
our side and make it complete and write its value from the table given
above, and the obtained value is the octal number.

1 101 100 011

equivalent octal number 001 101 100 011
54 3

therefore (11011000112) = (15438) Ans.

Example : Convert binary number (101010101010100)2 into octal number.
Solution :
After writing binary number into the sets of three digits each and writing octal
number for them-

101 010 101 010 100

5 25 24

therefore (101010101010100)2 = (52524)8 Ans.

Octal - Binary Conversion Number System
NOTES
______________________________________________________________________________________
71
In the last section, we learnt how to convert binary into octal. We'll know in this section
how is octal binary conversion made. For octal binary conversion, we take the binary
number of each digit of the given octal number. The set of the same binary digits will be
the converted binary number form of the given octal number.

Example : Convert the octal number (65)8 into binary number.
Solution : Putting the binary value of octal numbers 6 and 5 -

65

110 101

therefore (65)8 = (110101)2 Ans.

Hexadecimal Number System

______________________________________________________________________________________

In the previous section you understood binary, decimal and octal number systems. In
addition you came to know how these three number systems are converted into each-
other. Now we will know what hexadecimal number system is. Hexa stands for six and
decimal stands for ten. Therefore Hexadecimal refers to 16. There are 16 digits in this
number system. Ten digits are those coming under decimal number system (0 to 9) and
the remaining 6, are the letters from A to F. The alphabets. A to F represent the numbers
from 10 to 15. Every hexadecimal digit represents 4 binary digits. (See the table 4.2)

There are total 16 digits in the hexadecimal number system. Therefore its base is 16. In
this number system the positional value will be as follows -

......... ← 163 ← 162 ← 161 ← 160

......... 4096 256 16 1

Hexadecimal Character Decimal Equivalent Binary Equivalent

0 0 0000

1 1 0001

2 2 0010

3 3 0011

4 4 0100

5 5 0101

6 6 0110

7 7 0111

8 8 1000

9 9 1001

A 10 1010

B 11 1011

C 12 1100

D 13 1101

E 14 1110

F 15 1111

Table 4-2 : Hexadecimal-Decimal-Binary Equivalent

Fundamentals of Hexadecimal - Decimal Conversion
Computers &
Information Technology ______________________________________________________________________________________

NOTES Do you know how hexadecimal numbers are converted into decimal number ? This section
will deal with the same to convert the number from hexadecimal to decimal each digit
72 of hexadecimal number is multiplied with its positional value, the sum of products is
found. The sum of the obtained products represents the decimal converted number of the
given hexadecimal number.

Example : Convert the hexadecimal number (4F6A)16 into decimal number.
Solution :
On multiplying each digit of hexadecimal number with its positional
value and writing this sum -

4 F 6A

4096 256 16 1

(4096 × 4) + (F × 256) + (6 × 16) + (A × 1)

= (4 × 4096) + (15 × 256) + (6 × 16) + (10 × 1)

= 16384 + 3840 + 96 + 10

= 20330

Therefore (4F6A)16 = (20330)10 Ans.

Example : Convert the hexadecimal number (A0119)16 into decimal number.

Solution : A 0 1 1 9

65536 4096 256 16 1

(A × 65536) + (0 × 4096) + (1 × 256) + (1 × 16) + (9 × 1)

= (10 × 65536) + (0 × 4096) + (1 × 256) + (1 × 16) + (9 × 1)

= 655360 + 0 +256 + 16 + 9

= 655641

vr% (A0119)16 = (655641)10 Ans.

Decimal - Hexadecimal Conversion

______________________________________________________________________________________

In this section we'll know about the steps used in decimal to hexadecimal conversion.
These are as follows :

ê The given decimal number is divided by 16, the base of hexadecimal number

system.

ê The obtained quotient is written below the decimal number and to the left

of the remainder.

ê After dividing the obtained quotient by 16 the new dividend is written below

the last dividend and the remainder is written to the right.

ê Similarly, the steps from 1 to 3 are repeated until the value of the dividend

becomes zero.

ê Now the obtained remainder (0 to 9 and A to F) is compiled in vertical (bottom

to top) order. This set of collected remainders is the hexadecimal converted form
of decimal number.

Example : Convert decimal number (20330)10 into hexadecimal number. Number System
Solution : NOTES

20330 dividend remainder 73

16 20330 10 or A
16 1270 6
16 79
16 4 15 or F
4
0

Therefore (20330)10 = (4F6A)16 Ans.

Binary-Hexadecimal Conversion

______________________________________________________________________________________

In this section you will know how binary numbers are converted into hexadecimal number
? From the right of the binary number given for conversion from binary number to
hexadecimal number, sets of 4 binary digits each are made. If there are less than 4 digits
in the last set, we put a zero from our side and make at a set of 4 digits. Now we write
the hexadecimal number of each group which has been given in table 4.2. Thus we obtain
hexadecimal number.

Example : Convert the binary number (1101101010011)2 into hexadecimal number.
Solution : Making the sets of 4 digits each in the given binary number -

1 1011 0101 0011

There is only one digit in the left most set, therefore we apply three zeros
to the left of it. According to table 4.2, 0011 = 3, 0101 = 5, 1011 = B,
0001 = 1, therefore,

0001 1011 0101 0011
1 B 5 3

Therefore (1101101010011)2 = (1B53)16 Ans.

Example : Find the hexadecimal-converted number of binary number (1000001)2.
Solution :
Dividing the digits of the given binary number into groups of 4 and writing
Example : their hexadecimal value from the table -
Solution :
0100 0001

41

Therefore (1000001)2 = (41)16 Ans.

Find the hexadecimal-converted number of binary number (11001100)2.

Dividing the digits of the given binary number into the sets of 4 digits each
and writing their hexadecimal value from the table -

1100 1100

CC Ans.
Therefore (11001100)2 = (CC)16

Fundamentals of Example : Find the hexadecimal number coming in place of the question mark
Computers & Solution : in equation (111110100001)2 = ( ? )16 .
Information Technology
Dividing the digits of the given binary number in the groups of 4 each
NOTES and writing their hexadecimal value from the table -

74 1111 1010 0001

FA 1

Therefore (111110100001)2 = (FA1)16 Ans.
Hexadecimal - Binary Conversion

Let us find out the way of converting hexadecimal into binary. For it, in the right to
left order of hexa-decimal number of every digit or letter, we first find the binary
equivalent value. The obtained group of 0 and 1 is the binary converted form of the
hexadecimal number. For example, there are three letters in ADD. Their binary
equivalent number can be found like this -

A D D
¯ ¯ ¯
1010 1101 1101

The binary equivalent of A is 1010 and of D is 1010. Thus the binary value of (ADD)16
will be-

Example : (101011011101)2
Solution :
Convert the hexadecimal number (CD)16 into binary number.

The binary equivalent numbers of the hexadecimal number C and D are
1100 and 1101 respectively. It can be written as follows to understand
better-

CD

1100 1101

Therefore, (CD)16 = (11001101)2 Ans.

Example : Hexadecimal (34A5)16 = ( ? )2. What should be written in place of the
question mark ?

Solution : Writing the value of the digits of given hexadecimal number from the table-

3 4 A5 Ans.
0011 0100 1010 0101
Hence (34 A5)16 = (0011010010100101)2

Decimal Binary Hexadecimal Octal
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 4 4
5 100 5 5
6 101 6 6
7 110 7 7
8 111 8 10
9 1000 9 11
1001

10 1010 A 12 Number System
NOTES
11 1011 B 13

12 1100 C 14

13 1101 D 15

14 1110 E 16

15 1111 F 17

16 10000 10 20

17 10001 11 21

18 10010 12 22

19 10011 13 23

20 10100 14 24

Table 4-3 : The value of different number systems

FRACTIONAL CONVERSION

Fractional Binary-Decimal Conversion

It is a bit more complex to convert fractional numbers. Let's see how it is done. For
fractional binary-decimal conversion, the binary part given before decimal symbol is converted
by binary-decimal conversion method, while the numbers writer after the decimal symbol
are written to the left in the order of (–1, –2, –3, –4, ......) in the following method.

2–1 2–2 2–3 2–4

Every digit of the binary number given like this is multiplied with their positional value, and
the sum of the product is obtained. This sum of products will be the number converted
into decimal.

Example : Convert (11.1010)2 into decimal number.
Solution : (11.1010)2 will first be divided into two parts like this-

n (11)2
n (.1010)2
n (11)2 will first be converted into decimal number :

11

1 × 21 1 × 20

1×2 1×1

Thus 2 + 1 = 3. Check Your Progress :
It means the decimal value of (11)2 will be (3)10 . 4. Convert the following into

11 hexadecimal number sys-
1×2 = 1 tem (1000001) .

1×2 = 2 2

3 5. What is hexadecimal
number
n Now (.1010)2 will be converted into decimal number :
6. What do you know about
2–1 2–2 2–3 2–4 Fractional Conversion of
Binary-decimal.
1 0 10
75
1 × 2–1 + 0 × 2–2 + 1 × 2–3 + 0 × 2–4

Fundamentals of 1×½ + 0×¼ + 1 × 1/8 + 0 × 1/16
Computers &
Information Technology 1 × .5 + 0 × .25 + 1 × .125 + 0 × .0625
.5 +0
NOTES + .125 +0

76 = (.625)

Therefore (11.1010)2 = (3.625)10
Example : Convert (0.111)2 into decimal number.

Solution : 2–1 2–2 2–3
1 11

1 × 2–1 + 1 × 2–2 + 1 × 2–3
1 × 1/8
1×½ + 1×¼ + 1 × .125
.125
1 × .5 + 1 × .25 + (.875)

.5 + 0.25 +

=

Therefore, (0.111)2 = (0.875)10

Fractional Decimal-Binary Conversion

How is fractional decimal to binary conversion done ? For fractional decimal-binary conversion
the number before the decimal symbol given in the fraction is converted by the same
method of converting decimal number into binary number. And the number coming after
the decimal symbol will be multiplied with 2, the base of binary, until the number before
the decimal symbol becomes zero or till it is found it will never turn zero.

Example : Convert (16.125)10 into binary number.
Solution : First, it will be divided into two parts :

n (16)10
n (.125)10
n (16)10 =

2 16
2 80
2 40
2 20
2 10

01

(10000)2

n (.125)10 = .125 × 2
0 .250 × 2
0 .500 × 2
1 .000

(.001)

Therefore (16125)10 = (10000.001)2

Example : Convert (3.625)10 into binary. Number System
Solution : First, we'll divide it into two parts : NOTES

(i) (3)10 (ii) (.625)10 77
n vc (3)10 = 23

2 11

01

n (.625)10 = (11)2
.625 × 2
1 .250 × 2

0 .500 × 2

1 .000

(.101)2
Therefore (3.625)10 = (11.101)2

Summary

l Computer doesn't interpret our instructions directly nor do we have the
capacity to understand the original instructions of the computer.

l Computer understands only 0 and 1 and all our instructions are turned into these two
digits, with the help of translator program. Again, when we need the instructions from
a computer, similarily the translator program converts it into a language understandable
on the user level.

l The operations based on number are called digital operations.
l Analog operations are those operations which don't use digits at all, but with the

alphabetical order of predefined values, express the data into convertible points.
l Earlier, computers were analog and most machines worked on the analog method.

Temperature measuring device, thermometer is a popular example of analog operation.
l The base of computer operation is 2 which is called binary.
l 0 and 1 are called binary digits.
l Binary digits are called bit in short.
l Four bits make one nibble.
l Eight bits make a byte.
l In binary number system, Two digits are 0 and 1 and the number of all their digits

is 2. Therefore, the base of this number system is 2.
l In decimal number system, there are 10 digits from 0 to 9. The base of this

number system is 10 as it has total 10 ten symbols or digits.
l To convert a binary number into a decimal number each digit of the binary

number is multiplied with its positional value and a sum of the product is derived.
This sum of products is the equivalent decimal number of that binary number.
l There are total 8 digits (0, 1, 2, 3, 4, 5, 6, 7) in octal number system. Therefore,
the base of this number system is 8.
l Hexa means 6 and decimal stands for 10. Thus, Hexadecimal refers to 16. In this
number system, there are 16 digits. Ten digits are from 0 to 9 coming under
decimal number system and the remaining 6, are the letters A to F from Alphabet.

Answer of the Check your progress :

1. The operations based on number are called digital operations–Analog opera-
tions are those operations which don't use digits at all, but with the alphabetical order
of predefined values, express the data into convertible points. Earlier, computers
were analog and most machines worked on the analog method. temperature mea-

Fundamentals of suring device, thermometer is a popular example of analog operation.
Computers & 2. Symbol Value : These are the digits from 0 to 9.
Information Technology
Positional Value : The right to left direction of the number, in the order of the power
NOTES of base 10- such as thousand, hundredth. Tenth, unit etc. increases.
These are arranged as follows :
78 thousands ← hundred ← tenth ← unit
The position of the negative digits goes from right to left and starts from 0.
Such as .......... ← 3 ← 2 ← 1 ← 0
3. (83 × 1) + (82 × 2) + (81 × 0) + (80 × 4)

(512 × 1) + (64 × 2) + (8 × 0) + (1 × 4)
= 512 + 128 + 0 + 4
= 644

Therefore (1204)8 = (644)10

4. Dividing the digits of the given binary number into the sets of 4 digits each and writing

their hexadecimal value from the table -

1100 1100

CC
Therefore (11001100)2 = (CC)16
5. Hexa means 6 and decimal stands for 10. Thus, Hexadecimal refers to 16. In this number
system, there are 16 digits. Ten digits are from 0 to 9 coming under decimal number
system and the remaining 6, are the letters A to F from Alphabet.
6. For fractional binary-decimal conversion, the binary part given before decimal symbol is
converted by binary-decimal conversion method, while the numbers writer after the
decimal symbol are written to the left in the order of (–1, –2, –3, –4, ......) in the
following method.

2 2 2 2–1 –2 –3 –4

Every digit of the binary number given like this is multiplied with their positional value,
and the sum of the product is obtained. This sum of products will be the number converted

into decimal.

Exercise

1. What are digital operations ?

2. Explain analog and digital operations.

3. Explain binary data.

4. What are binary digit ? What is it called in brief ?

5. What are Nibble and byte ?

6. How many bytes have been used in 'I am a student' ?

7. Represent the word 'MANSOOR' in binary.

8. How many digits are there in binary number system ?

9. How many digits are there in decimal number system ?

10. Explain the rules of decimal-binary conversion.

11. Explain octal number system.

12. Do computer manufacturers use octal number system ?

13. Write the rules of converting octal into decimal.

14. Explain hexadecimal number system.

15. How will you convert a binary number into a hexadecimal number.

16. Convert (10.1110)2 into decimal number system.
17. Convert (8.025)10 into binary number system.
18. Convert the following into decimal number system.

(i) (1101)2 (ii) (567)8
(iii) (10A)16 (iv) (10010)2
19. Convert the following into Octal Number System.

(i) (109)10 (ii) (1101)2
(iii) (10B)16 (iv) (10010)2
20. Convert the following into hexadecimal number system.

(i) (1101)2 (ii) (1234)8
(iii) (20D)16 (iv) (12345)10

5 Data Representation and Data Representation
and
Binary Arithmetic
Binary Arithmetic
The Chapter Covers :
NOTES
n Introduction
n Bits, Nibbles, Bytes and Words
n Data Representation
n Coding system
n Binary Arithmetic
n Binary Addition
n Binary Subtraction
n Binary Multiplication
n Binary Division
n Character Representation
n Checking the Result of Binary Arithmetic
n Summary
n Exercise

INTRODUCTION

Binary arithmatic system refers to the arithmetic system, used by computer on its level.
This chapter encapsulates all the four operations of binary arithmetic, addition, subtraction,
multiplication and division have been presented. In addition to it, character representation
and coding system have also been discussed.

79

Fundamentals of BITS, NIBBLES, BYTES AND WORDS
Computers &
Information Technology Let us define bits, nibbles, bytes and words in the beginning of this chapter. Computer
understands instructions only in the form of 0 and 1. 0 and 1 are called system digits.
NOTES 0 or 1 is called bit which is the abbreviated form to binary digit. Eight binary digits make
a byte. One byte represents a character. Bytes are denoted by their EBCDIC coding
80 systems. For example, the storage space of the computer based on EDCDIC or ASCII 8
codes is made of magnetic or light media of electronic circuit elements, which can
represent at least 8 bits. Thus every storage space can have one character. The capacity
of primary and second ary storage devices of the computer is generally represented in
bytes.

A word is a combination of bits and it is, in general, bigger than a byte and is shifted
between primary storage and A.L.U. register and control unit. Thus a computer with the
length of 32 bit word can have a register of 32 bit capacity and it transfers data and
instructions in the set of 32 bits inside the CPU. These computers are faster than those
with 8 and 16 bits.

System digit = 0 and 1 = 8 bit
Binary digit (bit) = 0 or 1
1 nibble = 4 bit = 1,048, 576 byte
1 byte = 2 nibble = 1,073, 741, 824 byte
1 Kilobyte = 1024 byte
1 Megabyte = 1024 kilobyte
1 Gigabyte = 1024 megabyte

Table 5.1 : Memory Measurements

DATA REPRESENTATION

What is data representation ? As we know, computer understand only digits and that only
0 and 1. 0 and 1 stand for two conditions. In computer data is represented on the basis
of the state of the electronic switch. As we light the bulb with a switch, it has two
conditions. The moment you put the switch on, the bulb is lit and the moment you switch
it off, it is off. Likewise a computer too has switches which represent the probable
conditions on and off. When the switch is off in computer, it denotes 0 and when the
switch is on, it denotes 1. Thus, it may be said that the base on which a computer works
is 2 which is called binary.

0 and 1 are called Binary digits. The binary digits are called bit in short. 4 bits make a
nibble and eight bits create a byte. One byte represents one character or space. More than
one bytes create a word. For examle there is an eight byte word COMPUTER and it can
be expressed in binary data like figure 5.1.

C 0100 0011
O 0100 1111
M 0100 1101
P 0101 0000
U 0101 0101
T 0101 0100
E 0100 0101
R 0101 0010

Fig. 5-1 : The binary representation of the word COMPUTER

CODING SYSTEM Data Representation
and
What is coding system and how many types of them are there in vogue ? We know that
computer works through binary numbers, and therefore it is necessary to convert the Binary Arithmetic
numbers, characters and other symbols into binary numbers. We have read about conversion NOTES
of the number systems but it is not enough to understand the collection of data and
information for processing in the computer. It means binary information must be an 81
specific condition for storage and processing in the computer. Every key pressed on the
keyboard of a computer gives the message input of one character. The digits from 0 to
9, the alphabets from A to Z or specific characters +, –, *, /, ?, \, >, < etc. are in total
256 characters. There is a specific binary number for each character. In computer to
represent the characters, there are different codes of binary numbers. such as- ASCII,
EBCDIC, BCD etc. Every code to denote a character provides a certain number and
arrangement of binary numbers.

ASCII – American Standard Code for Information Interchange

In ASCII for 128 characters, there are codes with 7 binary digits (bit). It means for
each character, there are 7 bits. This code or symbol has two parts : the 4 bits of right
are the numeric part and the 3 bits of left are called zone. Most of the microprocessor
and IBM PC use the ASCII code.

There is a decimal number for every character- digits from 0 to 9, characters for A-
Z, a-z and symbols +, –, *, {, }, /, \, >, etc. which is called ASCII value of that
character. This has been given to total 256 characters from 0 to 255. The ASCII
symbols of different characters have been given in the table below.

EBCDIC – Extended Binary Coded Decimal Interchange Code

EBCDIC code express a character in 8 binary digits. It contains total 256 various codes
for all 256 characters. One EBCDIC code has two parts.

The first Numeric part represents 4 bits from the right. Second is Zone Part which
expresses 4 bits from the left.

EBCDIC coding system is used in Mainframe computers of IBM and other big computers.
The table ahead also contains different EBCDIC symbols.

Character Standard BCD EBCDIC ASCII
Intercharge Code
0 11110000 0110000
1 1001010 11110001 0110001
2 0000001 11110010 0110010
3 0000010 11110011 0110011
4 1000011 11110100 0110100
5 0000100 11110101 0110101
6 1000101 11110110 0110110
7 1000110 11110111 0110111
8 0000111 11111000 0111000
9 0001000 11111001 0111001
A 1001001 11000001 1000001
B 0110001 11000010 1000010
C 0110010 11000011 1000011
D 1110101 11000100 1000100
E 0110100 11000101 1000101
1110101

Fundamentals of F 1110110 11000110 1000110
Computers &
Information Technology G 0110111 11000111 1000111

NOTES H 0111000 11001000 1001000

82 I 1111001 11001001 1001001

J 1100001 11010001 1001010

K 1100010 11010010 1001011

L 0100011 11010011 1001100

M 1100100 11010100 1001101

N 0100101 11010101 1001110

O 0100110 11010110 1001111

P 1100111 11010111 1010000

Q 1101000 11011000 1010001

R 0101001 11011001 1010010

S 1010010 11100010 1010011

T 0010011 11100011 1010100

U 1010100 11100100 1010101

V 0010101 11100101 1010110

W 0010110 11100110 1010111

X 1010111 11100111 1011000

Y 1011000 11101000 1011000

Z 0011001 11101001 1011010

Table 5-2 : Different values of Data Representation

Decimal Digit Binary Digit The ASCII value of character
A is 65. 65 is a decimal
0 0000 number whose binary
1 0001 equivalent number is
2 0010 (1000001)2, therefore A is
3 0011 represented by 1000001.
4 0100
5 0100
6 0110
7 0111
8 1000
9 1001

Table 5-3 : Decimal binary value table

Binary Coded Decimal

Every decimal digit is represented by 4 binary digits. The binary numbers from 0 to
9 have been fixed according to the decimal binary value table given above. Here BCD
stands for - Such decimal digits which have been converted into binary code.

Example, Decimal number 1981 is represented in BCD codes like this :

Decimal state 1 9 8 1
BCD state 0001 1001 1000 0001
Therefore, 1981 = 0001 1001 1000 0001

Here, it is noteworthy, that this method is quite different from the one for converting form
Decimal number to binary number.

Unicode Data Representation
and
There will be as many scripts as there will be languages in the world. Do you know
a person who knows all the languages as well as the scripts of the world? It might be Binary Arithmetic
possible only for the God. Then, have you ever thought that the computer is being NOTES
operated almost the entire world and in many international and regional languages. For
example, in India itself, computer is being operated in Hindi, Telgu, Tamil, etc. After Check Your Progress :
all, how is it possible? To enable the computer in doing this, a coding system has been 1. What is Binary digit ?
developed in computer. Because of ASCII, E B C D I C, B C D coding systems, 2. What does ASCII and
computer is successfully operating in different languages. But, today, to run the computer,
these coding systems were not enough. Just to overcome this, the Unicode was born. EBCDIC stands for ?
3. Define UNICODE.
Unicode can be understood as Uniform Code or Universal Code. Unicode is a coding
standard which is used for computer processing to represent the text. Under this 83
coding system, there is a unique number for every character. No matter what platform
or language this character is from. UTF-8, UTF-16 and UTF-32 are unicode standards
in three ways. The complete form of UTF is Unicode Transformations format. UTF-8
is a byte based format, while UTF-16 and UTF-32 are based on 1 and 2 respectively.
To avail more information in this regard, you may log on to www.unicode.org.

BINARY ARITHMETIC

In binary arithmetic, like other arithmetics, there are four operations- addition, sub-
traction, multiplication and division. It is similar to that of decimal arithmetic. However,
the binary arithmetic method is a bit complex, as the entire operation is based on 0
and 1 and we are hardly used to it in our day to day life.

Binary Addition

The binary addition is similar to that of simple decimal numbers. We only need to
remember a few facts related to it, which are as follows :

0 + 0 = 0 (nothing carried)
1 + 0 = 1 (nothing carried)
0 + 1 = 1 (nothing carried)
1 + 1 = 0 (1 carried)

Now we will understand binary addition with decimal addition. For example we have
to add 6 and 7. The binary equivalent of 6 is 0110 and the binary equivalent of 7
is 0111. Now we add the both.

Decimal Binary

1 (carry) 110 (carry)
06 0110
07 0111

13 1101

Fig. 5-2 : Decimal-Binary addition

Let us understand the binary addition gives in figure 5.2 above, in a more simplified
way. In this, we have to add 0110 and 0111. For it, we add the digits separately. The
process of addition goes from right to left. Therefore, it will be done as follows :

0 +1 =1 (nothing carried)

0 + 1 + 1 = 0 (carry 1, which is added to different digits.
It can be understood like 1+1 = 10.)

1 + 1 + 1 = 1 (In it, 1+1 = 10 and if we add 1, becomes 11,
it means 1 carry which will be carried to the next.)

Thus, (0110)2 and (0111)2 if added, the sum will be (1101)2 .

Fundamentals of Likewise, let us see one more example - Binary (carry)
Computers &
Information Technology Decimal 1101
1101
NOTES (carry) 0101
13
84 05 10010
18

In the sections ahead, a few examples related to it have been given :

Example : Add 1011001 to 11001.

11 1 ← carry

1011001
+ 11001

1110010

Example : Add 1110 and 1010. ← carry
111
1110

+ 1010

11000

Example : Add 11100 and 10001.

1 ← carry

011100
+0 1 0 0 0 1

101101

Example : Add 110011 and 1101 and get the sum.

111111 ← carry

110011
+ 001101

1000000

Example : Add 1111 and 101. ← carry

1111
1111

+ 0101
10100

Example : Add 101101 and 1111. ← carry Data Representation
and
1111
101101 Binary Arithmetic
+0 0 1 1 1 1 NOTES
111100
85
Example : Add 1111011 and 11011. ← carry

1111011
1111011

+ 0011011
10010110

Binary Subtraction

Binary Subtraction is also like decimal subtraction in which, we borrow from next digits.
The facts related to it are as follows :

0 – 0 =0

1 – 0 =1

1 – 1 =0

0 – 1 = 1 (on borrowing from next digits)

For example, have a look at the subtraction process of both types of numbers -

37 – 17 = 20 100101 – 10001 = 10100

Decimal Binary

(nothing borrowed) (1 borrowed)
1
37 100101
–17 –010001

20 10100

Likewise, now, look at the following example : 110011 – 10110 = 11101
51 – 22 = 29
Binary
Decimal
0 10 1
4 5 →11 1 1 0 10 1 1
1 – 10110
011101
–22

29

Fundamentals of To understand it, a few examples have been given :
Computers & Example : Subtract 101 from 1101.
Information Technology 1101
–0101
NOTES 1000

86 Example : Subtract 1001 from 1110.

10
1 110
– 1001
0101

Example : Subtract 1010 from 1100.

10
1100
– 1010
0010

Example : Subtract 11011 from 1111011.
1111011

–0011011
1100000

Example : Subtract 101110 from 1010110

10 10
1010110
– 0101110
0101000

Example : Subtract 1001101 from 1011110

10
1011110
– 1001101
0010001

Example : Subtract 100010 from 101011.
101011

–100010
001001

Binary Multiplication Data Representation
and
Binary Multiplication is similar to that of decimal multiplication. When multiplying, their
sum is similar to that of binary sum. The product is clear through the following facts : Binary Arithmetic
NOTES
0 ×0 =0
0 ×1 =0 87
1 ×0 =0
1 ×1 =1

Here we display this with respect to the product of the decimal digits :

Decimal Binary

41 101001
×6 ×1 1 0
246
000000
101001
101001

11110110

Similarly have a look at this example : Binary
Decimal
10111
1 ×1 0 0
23
×4 00000
92 00000
10111

1011100

Example : Find the result of 1100 × 1101.

1 1 0 0×1 1 0 1

carry → 11

1100
0 0 0 0×
1 1 0 0 ××
1 1 0 0 ×××

10011100

Example : Find the product of 111 × 1100.

0 0 1 1 1×1 1 0 0

carry → 111

00000
0 0 0 0 0×
0 0 1 1 1 ××
0 0 1 1 1 ×××

01010100

Fundamentals of Example : Find the product of 110011 × 101.
Computers &
Information Technology 1 0 0 1 1×1 0 1

NOTES 110011
0 0 0 0 0 0×
88 1 1 0 0 1 1 ××

11111111

Example : Find the product of 101010 and 100.

1 0 1 0 1 0×1 0 0

000000
0 0 0 0 0 0×
1 0 1 0 1 0 ××

10101000

Example : Find the product of 1101 and 111.

0 1 1 0 1×1 1 1

rest → 1 1 1 1

01101
0 1 1 0 1×
0 1 1 0 1 ××

1011011

Example : Find the product of 1001 and 1000.

1 0 0 1×1 0 0 0

0000
0 0 0 0×
0 0 0 0 ××
1 0 0 1 ×××

1001000

Binary Division

Binary division is the repeated process of subtraction, as it happens with decimal division.
For example,

101010 ÷ 110 = 111

It is done as follows : 111 = 07

)1 1 0 110 1 0 1 0 = 42
= 06
–110

1
1 0 10 1

–110

×× 1 1 0
–110
×××

Example : Find the quotient of 1000011 and 101. Data Representation
and
10000111 ÷ 101 = 11011
Binary Arithmetic
135 ÷5 = 27 NOTES

It will be done like this : 11011 = 27 89

)1 0 1 1 0 0 10 0 1 1 1 = 135
= 05
–101

110
–101

11
–0

111
–101

101
–101

0

CHARACTER REPRESENTATION

What is character representation ? We apply plus (+) or minus (–) before the number
to represent its symbols. Such symbols can't be used in computer. Another method is
used for it. To represent a positive number one adds a zero (0) before a binary number
and to adds 1 before a binary number. For example, +15 and –15 are respectively
written as 01111 and 11111. There is only one method to represent a positive number,
but to represent a negative number, there are several methods. These are -

n Signed – magnitude representation

n Signed – 1's complement representation

n Signed – 2's complement representation

–15 can be expressed in all three above mentioned modes as11111, 10000, 10001
respective. Since –15 has been represented in 4 bits to represent the sign 1 bit has been
used additionally, the MSB (Most Significant bit), to represent the number sign.

For example, a computer with 8-bits represents –15 is signed-magnitude as 10001111, in
signed 1's complement as 10000000 and in signed 2's complement as 10000001. The seven
bits are used to represent the number and MSB is used to represent the number sign.

When all the bits of a computer (8 bits- the length of a word in computer is 8 bits) are
used to represent a number and a bit is not used to represent a sign, it is called un-signed
representation of the number.

CHECKING THE RESULT OF BINARY ARITHMETIC

Suppose, you have a doubt regarding number system conversion or binary arithmetic, you
can check it on your own computer. Let's us see, how you would testify the result of
binary arithmetic on computer ? You can test the result of binary arithmetic with the
calculator of your computer. For this, follow the following instructions.

Fundamentals of ê Click Start.
Computers &
Information Technology ê Point to Programs.

NOTES ê Point to Accessories and select the Calculator.

90 ê From here click View menu and select Scientific.

ê Then click Bin radio button. And type binary number from the keyboard or

click the digits of the numbers with the numeric pad of the calculater.

ê Then to add it, press + on the keyboard or click the + sign of the calculator.

ê Then insert another number. Press enter key to view the result.

SUMMARY

l 0 and 1 are binary digits. Binary digits are called bits in short.

l 4 bits make a nibble and eight bits make a byte.

l In ASCII, there are 7-bit codes for 128 characters. It means for each character, there
are 7 bits.

l For every character- digits from 0-9, alphabet letters from A-Z, a-z and for the symbols
+, –, *, {, }, /, \, >, etc there is a decimal number, which is called ASCII value of
that character.

l EBCDIC symbols represent one character in 8 binary digits. In it, there are 256
symbols for all 256 characters.

l Unicode can be taken as Uniform code or Universal Code.

l Unicode is a coding standard which is used for computer processing for text repre-
sentation. Under this coding system, for every character, there is a unique number.
No matter whichever platform or language these characters belong to.

ANSWER OF THE CHECK YOUR PROGRESS :

1. 0 and 1 are called Binary digits. The binary digits are called bit in short. 4 bits
make a nibble and eight bits create a byte. One byte represents one character
or space. More than one bytes create a word.

2. ASCII — American Standard Code of Information Interchange.

EBCDIC — Extended Binary Code Decimal Interchange Code.

3. Unicode can be understood as Uniform Code or Universal Code. Unicode is
a coding standard which is used for computer processing to represent the text.
Under this coding system, there is a unique number for every character. No
matter what platform or language this character is from. UTF-8, UTF-16 and
UTF-32 are unicode standards in three ways.

4. Binary Arithmetic–In binary arithmetic, like other arithmetics, there are four
operations- addition, subtraction, multiplication and division. It is similar to that
of decimal arithmetic. however, the binary arithmetic method is a bit complex,
as the entire operation is based on 0 and 1 and we are hardly used to it in our
day to day life.

5. Binary Multiplication–Binary Multiplication is similar to that of decimal multipli- Data Representation
cation. When multiplying, their sum is similar to that of binary sum. The product and
is clear through the following facts :
0× 0 = 0 Binary Arithmetic
0× 1 = 0 NOTES
1× 0 = 0
1× 1 = 1 Check Your Progress :
4. What is Binary Arithmetic ?
6. For every character- digits from 0-9, alphabet letters from A-Z, a-z and for the 5. Write something about
symbols +, –, *, {, }, /, \, >, etc there is a decimal number, which is called
ASCII value of that character. Binary Multiplication ?
6. What is ASCII value ?
EXERCISE
91
1. Explain coding system in detail in computer.
2. What do you mean by American Standard Code for Information Interchange ?
3. Explain Unicode.
4. What is binary arithmetic ?
5. What is the difference between binary addition and decimal addition.
6. Explain the complete process of binary addition ?
7. Is the sum of 1 and 1, 10 is binary addition ?
8. Explain the entire process of binary subtraction.
9. Can be subtract 45 and 10 in binary subtraction ?
10. Explain the entire process of binary multiplication with an example.
11. Explain the entire process of binary division with an example.
12. What do you understand by character representation ?
13. What is the process of testifying the result of binary arithmetic on the com-

puter ?
14. Add the following in binary method.

(i) 1101 + 1111
(ii) 1011 + 101
(iii) 0100 + 100
(iv) 1111 + 1001
15. Subtract the following in binary method.
(i) 1001 - 110
(ii) 1001 - 1000
(iii) 1111 - 1101
(iv) 10011 - 1100

Fundamentals of 16. Multiply the following in binary method.
Computers & (i) 1100 x 110
Information Technology (ii) 1100 x 1100
(iii) 00111 x 110
NOTES (iv) 110011 x 1001

17. Divide the following binary method.
(i) 100010 ÷ 110
(ii) 1110 ÷ 11
(iii) 1001 ÷ 101
(iv) 1110 ÷ 100

92

6 Input Devices Input Devices
NOTES
The Chapter Covers :
 Introduction
 Input Device
 Typing Input Devices
 Pointing Input Devices
 Scanning Input Devices
 Audio Visual Input Devices
 Summary
 Exercise

INTRODUCTION

Input devices are like our hand and feet thought which we input our labor. Likewise, in
computers there are a number of input devices. These devices instruct the brain of
computer about what to do. Input devices are available in different forms and all have
some specific purposes. For typing, we have keyboard that makes us type our instructions.
Mouse that helps us execute commands by clicking and double clicking. This is also used
for selecting and deselecting. Joystick, trackball are more or less identical to mouse.
Scanner inputs images to CPU. Moreover, there are also devices for inputting audio and
video. This chapter gives a complete coverage for each input device so far available in
the market.

93

Fundamentalsof INPUT DEVICE
Computers &
Information Technology Let us start this chapter with knowing about what input devices are. Input devices are
those devices which take our commands to the CPU of the computer. Keyboard, Mouse,
NOTES Scanner etc. are popular input devices. The types of input devices have been shown in
figure 6.1.

Input Devcie

Typing Pointing Scanning Audio Visual

Mouse Image Voice Recognition
Key-board
Optical Charac-
Joystick
Microphone

Terminals Trackball

Optical Mark

Touch Digital Camera

Magnetic Ink Character Recognition

Light Bar Code Reader

Digitising

Fig. 6.1 : Types of Input Devices

TYPING INPUT DEVICES

Typing input devices are the input devices of a computer which are used to input the data
by typing it. Keyboard and terminals are such devices however the terminal is a bit out
of the way.

Keyboard

A computer keyboard is a peripheral partially modelled as per the typewriter keyboard.
Keyboards are designed for the input of text and characters and also to control the
operations of a computer.

94

Fig. 6.2 : Parts of Keyboard

Physically, computer keyboards are an arrangement of rectangular or near-rectangular Input Devices
buttons, or “keys”. Keyboards typically have characters engraved or printed on the NOTES
keys. In most cases, each press of a key corresponds to a single written symbol.
However, producing some symbols requires pressing and holding several keys simul- 95
taneously or in sequence. Other keys do not produce any symbol, but instead affect
the operation of the computer or the keyboard itself.

Roughly 50% of all keyboard keys produce letters, numbers or signs (characters). Other
keys can produce actions when pressed, and other actions are available by the simulta-
neous pressing of more than one action key.

Anatomy of a keyboard

We can classify the keys of keyboard in six types to understand its anatomy as-

 The Alphanumeric Keys
 The Numeric Keypad
 The Function Keys
 Special Purpose Keys.
 The Modifier Keys
 Cursor Movement Keys

The Alphanumeric Keys

The alphanumeric keys are centrally located in a keyboard as you see in a
traditional manual typewriter. The alphanumeric keys include alphabet (A - Z or
a - z), numeric characters (0 to 9), special symbols ( ~ !@# $%^ &* ()_+ | \= -). The
arrangement of the keys in this section of a keyboard is called QWERTY (pronounced
QWER-tee) arrangement as the top row of this section contains Q-W-E-R-T-Y letter.
Besides the digits, symbols and alphabets, there are four keys namely TAB, CAPS
LOCK, BACKSPACE and ENTER for some specific tasks.

The Numeric Keypad

The numeric keypad includes a set of 17-keys containing
0-9 digits, mathemetical operators, arrow keys, and some
special keys (Home, Pg Up, Pg Dn, End , Ins , Enter and
Del) . Special keys are locked and unlocked , pressing
Num Lock key. It workslike a calculator on your computer.

The Function Keys

On the upper side of keyboard there are 12 Function Fig. 6.3 : Numeric Keypad
keys denoted by F1, F2,.....F12. These keys let you use
commands in a short cut manner. Functions of these keys
change from software to software. However, F1 remains
for Help in most of the softwares commonly used.
Special Purpose Keys

With the advent of advanced softwares, keyboards have been equipped with special
keys which work according to new programs in operating system. These are Sleep,
Power, Volume, Start, Shortcut etc.

The Modifier Keys

There are three keys namely SHIFT, ALT (Alternate), CTRL (Control) that have no
prominent use when they are pressed alone. However, when they combine with
some other keys they change the input of those keys and therefore called as modifier
keys, Like when you hold down SHIFT key with A (When CAPS LOCK is Off) capital
A is input while in normal case small a is displayed. Similarly, when you use CTRL with
C it turns into a command used to copy the contents. ALT key helps you invoke
menus in the windows based programs.

Fundamentalsof The Movement Keys
Computers &
Information Technology There are four UP, DOWN, LEFT and RIGHT keys used to move cursor across the
screen. You can also find these keys in the numeric keypad but they can only be used
NOTES when NUMLOCK is ON.

96 Wireless Keyboard

In order to relieve users from wire in a Fig. 6.4 : Wireless keyboard with a
keyboard, some companies have launched mouse and their receiver
wireless keyboards. Though these
keyboards have freedom to use from a
limited distance, they are not in vogue
because of some technical complexity. In
most cases, a wireless keyboard is coupled
with a mouse and managed by its receiver
that controls both the keyboard and the
mouse. (See Figure 6.4)

Positive and Negative Aspects :

There can be following Positive and Negative aspects of a wire-less key-board

Positive Aspects :
 Free from wire
 Saving of desk space
 Key-board portability

Negative Aspects : Technical complexity
Comparative costlier
 Less durable



Ergonomic Keyboard

Many companies have developed ergonomic
keyboards, which give more comfort. These are
specially meant for enhancing work efficiency
and relieving the users from wrist injuries
developed due to incessant typing work.

Terminals Fig. 6.5 : Ergonomic Keyboard

Let us know what a terminal is, and how many types Fig. 6.6 : Terminals
of terminals are there. It is an uncommon input
device which is probably used either with a mini
computer or mainframe computer. It has a monitor
and a keyboard and is attached to the remote
computer. It is used to input data and obtain data
from the remote computer. It seems to be like a
desktop computer and you must have seen it in a
railway station or bank. Some terminals are fix while
a few can be taken from one place to another. Dumb,
smart and intelligent are types of terminals.
Dumb Terminal

It is the most low cost terminal and is completely based on the main computer. It does
not have self processing power. It can input data only with the help of a key-board and
can obtain data from the main computer for information which is displayed on the screen.
The computers that you see on the railway reservation, is a dumb computer.

Smart Terminal Input Devices
NOTES
Smart Terminal has, besides the capacity to input and obtain data, some limited
processing powers. One can't write or program a new instruction into it. Point of sale Check Your Progress:
terminal is a very popular smart terminal which is like a cash register and it also accepts 1. How will classify the key-
sales and inventory data of sales point which is sent to central computer for processing.
Big Bazars and Vishal Mega Marts etc. use the same terminal. They keep updating sales boardin types.
and inventory information to the main computer every-minute. Such terminals have a 2. What isfunctionskey ?
bar-code reader, a key-board like a cash register, a cash drawer and a printer. In 3. What are the Positive and
banking, we see the use of the same kind of terminals.
Intelligent Terminal Negativeaspectsof awire-
Intelligent Terminal, in addition to data input, data acquisition has additional independent less keyboard?
processing capacity. It contains apart from keyboard, monitor and main computer link,
processing units, storage units and software. Such computers are used by big companies 97
in their branch offices where the branch managers manage it. Usually, micro-computers
are used as Intelligent terminals.

POINTING INPUT DEVICES

Pointing input devices are such devices which input commands by pointing to them.
For example, instead of typing a command to copy a text an icon of copy command
is pointed at and selected. Mouse, Light pen, touch screen and digitising tablet are the
examples of Pointing input devices.

Mouse

In 1980s, keyboard was probably the only device used as an input device with
computer. Since few years, especially when graphical user interface based computer
softwares and operating systems came in use, personal computers started coming with
a mouse as a pointing device. Most likely, it was named so because of its small size
in comparison with other main parts of computer like monitor and CPU cabinet.
Mouse is an online input device which can be used by single hand. By moving a mouse
on a plane surface, a ball inside the mouse rolls which in turn moves the rollers in-
built in the mouse.
Mouse was devised by Douglas Engelbart of Stanford Research Center in 1963, was
one of the most important inventions in the field of computer comforts, which took
place many important functions of keyboard and freed the users from monotony.
Mouse has two or more buttons. Left hand side button is most in use while right hand
side button is used in special cases sufficing special purposes. By the way, you can easily
change it with the help of the options available in the operating system software. On
pressing the button of mouse you can select the icons on the screen. The pressing of
button of mouse by finger is called "clicking". A mouse is generally used to navigate
pointer on the screen and to draw pictures and graphics.

Functions of Mouse

Mouse points you to a specific icon, menu or a particular location on the screen.
However, pointing alone can not make a mouse useful for the users. It performs five
major functions which you can not do with a keyboard, so comfortably. These are as
follows :

 Clicking
 Right Clicking
 Double Clicking
 Dragging
 Scrolling

Fundamentalsof Click
Computers &
Information Technology Scroll Button
Right click
NOTES

Figure 6.7 : Clicking parts of

 Clicking : Clicking or single clicking usually refers to pressing left button of the
mouse. When you point on object and click, the object is selected. It varies in
execution. For example, when you point to File menu and click, it is not selected,
rather the object is executed and opens its sub menus. While when you click an
icon on your desktop, it is selected though it depends how the desktop is
customized.

 Double Clicking : Double clicking means pressing left button of the mouse two
times incessently. Double click is mainly used to execute objects in icon forms.
When you point to a menu there is no need of double clicking.

 Right Clicking : Right clicking means pressing the right button of the mouse. It
is used to execute pop-ups or shortcut menus. For example when you point an
object and right unit you can get some very useful commands like copy, cut &
rename to copy, move and rename the object respectively. However, if you wish,
you can invert the functions of left and right buttons of the mouse by customizing
its properties.

 Dragging : Dragging means taking an object from one place to the other. This is
specially used when you are using windows explorer as a short-cut to Copy and
Move functions. You can also use this for any office application like you can move
and copy a block by dragging in Word or Excel. To use this, just point to the object
and click the left button if you have not changed setting of the mouse buttons and
do not release. Just holding the button take it to the place desired and drop (means
release the button). Where there is dragging there is dropping hence the method
is called drag and drop.

 Scrolling : There is a scroll button between both the buttons in a mouse. It is used
to scroll the matter on the screen up and down. This button is usually, not useful
in all the programs.

Types of Mouse

There are three types of mouse - Figure 6.8 : Mechanical Mouse
 Mechanical Mouse
 Optical Mouse
  Cordless Mouse

Mechanical Mouse – Most of the mice we see today
are mechanical mouse. This type of mouse, commonly
used on personal computers, has a small rubber ball
inside the case and can roll in all directions. Within the
mouse case, mechanical sensors perceive the direction
the ball rolls and move the pointer accordingly. (See
Figure 6.8)

Optical Mouse – Optical mouse is a new type of non-mechanical mouse. It is quicker
but more expensive than the mechanical one. It emits a beam of light from its underside.
It detects the distance, direction and speed of mouse with its reflection. (See Figures 6.9
98 and 6.10)

Input Devices
NOTES

Figure 6.9 : Upper part of optical mouse Figure 6.10 : Lower part of optical mouse

Cordless Mouse – Cordless Mouse being the most advanced technology, relieves you
from the botheration of wire. It uses radio frequency to communicate information to your
computer. It consists of two main components transmitter and receiver. Transmitter is
available in the mouse that sends information of the mouse movement and its clicking
action in the form of electromagnetic signal. Receiver, attached to your computer, receives
the signals, decodes them and sends them to mouse driver software and the operating
system being used on your computer. Receiver may be used separately or it may be used
as a card in any slot of motherboard. Some computers have got inbuilt receiver.

Figure 6.11 : Cordless Mouse and Receiver (R)

Joystick

Joystick is an input device generally used for playing Figure 6.12 : Joystick
video games. It has a handle which can help us in
navigating the turtle or graphics on the screen. This
generally is used to play games by children and hence
is a good medium to create interest of children in
computers. Although all the computer games can also
be played by keyboard but a joystick provides speed and
convenience in these games.

Track Ball

It has the same function as that of joystick and also used by kids. In lieu of a handle as
in the joystick, it has a ball on its upper surface, which on movement, navigates the cursor
on the screen. Track ball has the same operative mechanism like a mouse, but its use is
a bit simpler, therefore it is widely used by children without much difficulty.

Figure 6.13 : Track ball 99

Fundamentalsof Touch Screen
Computers &
Information Technology Touch screen is an input device. It consists
of a type of display screen, which allows the
NOTES user to place a finger instead of a pointing
device directly on the screen to select a
100 menu or object. Even the user not having
enough knowledge of computer can use it
very easily. Touch screen is undoubtedly a
very user friendly input device but cannot
help us input huge data in the computer.

Figure 6.14 : Touch Screen

Light Pen

Figure 6.15 : Light Pen It is also called electronic pen on stylus. Light pen is
used to draw any picture or graphics on the computer
screen. A light pen consists of a light-sensitive penlike
device to select objects on a display screen. Any graph-
ics drawn using light pen can be saved into computer
and can even be modified and resized. It is used in
PalmTop computers, e.9. Tablet P.C., Personal Digital
assistants and modern mobile devices.

Digitizer Tablet or Graphics Tablet

Digitizer tablet or graphics tablet is a drawing Figure 6.16 : Digitizer Tablet
surface with a mouse or pen. The drawing
surface has a complex network of wires. This
wire network receives the signal produced due
to the motion of mouse or the pen and sends
them to computers. This is used to input hand-
made characters directly to computers. It is
incorporated with a scanning head called a
"Puck". The puck is used to get the desired
graphical position of the character.

There is a complex network of chords in tablet or drawing level. It receives the signals which
are produced as a result of the motion of a cursor or a pen and sends it to a computer.
If you are a good painter used to a painting brush and want to save your figure in the
computer, you don't need a mouse. You can draw and save a figure in a computer as you
do with a paint brush.

SCANNING INPUT DEVICES

These are such input devices which complete data or commands through Scanning
Process. Scanner, Optical Character Recognigion, Optical Mark Reader, Magnetic Ink
Character Recognition are the examples of Scanning Input Devices.

Scanner

Scanner is the input device which inputs data on the paper in the form of graphics,
picture or text, directly into the computer. The biggest advantage of it is that one does
not have to type the data.
OCR, OMR, MICR all are examples of scanner. Besides these, there are special
scanners, called Image Scanners, which can input any photograph, graphics or pictures
in the computer memory in the digital form. Now-a-days, variety of scanners is
available for PCs with resolutions starting from 300 dpi ( dots per inch). Resolution
refers to the clarity of scanned picture. The number of dots in a unit area in a picture
is called resolution.