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TOPIC:

1.4 LOGIC GATE

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1. Logic diagrams are showing the wiring and connections of each individual logic gate that implements the
circuit.

a. Calculate the value of the following Boolean expression.

i. Y = A + C(B’·C), where A = 1, B = 0 and C = 1 [2 marks]

Y = 1 + 1(0’.1)
= 1 + 1(1.1)
= 1 + 1(1)
=1+1
=1

ii. X= (A+B)’ (B’+C), where A = 1, B = 0 and C = 0 [2 marks]

X = (1+0)’. (0’+0)
= (1)’ . (1+0)
= (0) . (1)
=0

b. Assume that x=1and y=2. Determine the value of the following Boolean expression and show the
working process.
i. (x=1) AND (y= 3)
[2 marks]

= True AND False
= False = 0

i. NOT ((x=1) AND (y=2)) [2 marks]

NOT ( (True) AND (True) )

NOT ( True )
False = 0

c. Draw logic diagrams for the following Boolean expressions: [4 marks]
i. Q = (X’ + Y) + (Y · Z)’

X

Y

Q

?Z

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ii. Y = (A’ + B)’ + (B·C’)’ [4 marks]

?A

B
Y

C
iii. Write the value for each stage of the logic diagram in Figure 1 below:

[2 marks]

A = 1, B = 0, C = 0

p

r

Figure 1

q s

Figure 1

p : ________________

P=0;q=1;r=0;s=1

iv. Based on logic diagram above, write Boolean expression to represent the circuit.
[2 marks]

W = (AC + B) (B’ + C)

v. Write the truth table for the logic diagram in Figure 1.

[4 marks]

A B C AC B’ B’+C AC+B W

000 0 1 1 00

001 0 1 1 00

010 0 0 0 10

011 0 0 1 11

100 0 1 1 00

101 1 1 1 11

110 0 0 0 10

111 1 0 1 11

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2. Logic gates are the basic components in digital electronics and are used to create digital circuits as well as
complex integrated circuits.
(a) Look at the truth table below.

Input A Input B Output

0 01

0 10

1 00

1 10

What logic gate does the table represent?

[1 mark]

NOR

(b)

?

(c) Figure 1 shows a logic circuit

Figure 1

i. Complete the truth table below for the logic circuit shown in Figure 1.

[3 marks]

Input A Input B Input C Output Q

101 0

010 0

011 0

110 0

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Two of the gates shown in Figure 1 could be replaced by a single gate. [2 marks]
ii. Which two (2) gates could be replaced?
[1 mark]
OR [4 marks]
NOT

iii. What single gate would be used instead?

NOR
(d) Name four (4) types of logic gate and complete their associated truth tables:

(e) Complete the truth table for the following logic circuit:

C’ = BC’ + AB [4 marks]

AB BC’
00
00 C C’ BC’ AB X
01 01 0 00
01 10 0 00
10 01 1 01
10 10 0 00
11 01 0 00
11 10 0 00
01 1 11
10 0 11

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(f) An engineer hands Aydaan a piece of paper with the following Boolean expression written on it,
and tells Aydaan to build a logic circuit that performs these function:

̅ + ̅ ( + )
Draw a logic gate circuit for this Boolean expression.

[5 marks]

3. Logic gates are the basic components in digital electronics and used to create digital circuits and even complex
integrated circuits.

a. Draw the logic gate based on the given Boolean Expression.
i. X = (A + B) C

[2 marks]

A A+B
B

X

C

ii. Produce the truth table for question 4(a)i. [8 marks]
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A B C A+B (A+B)C
00000
00100
01010
01111
10010
10111
11010
11111

b. A student is given a merit certificate if he gets a pass in all subjects or obtains an overall average
of 60 in his annual exam.

i. Draw a logic circuit that would allow a computer to decide which students should get a merit
certificate.

[1 mark]

P= pass all subjects
A= overall average of 60
S=merit certificate

P
S

A

ii. Produce the truth table for this circuit.

[4 marks]

PA S
00 0
01 1
10 1
11 1

c. For the following circuits, find the Boolean Expression and construct the truth table.

Y

i. Boolean expression Y= (A+B)’ + (AB) [1 mark]

ii. Construct truth table.

[4 marks]

A B (A+B) (A+B)’ AB (A+B)’ + (AB)

00 0 10 1
01 1 00 0
10 1 00 0
11 1 01 1

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4. Logic diagrams are shows the wiring and connections of each individual logic gate that implements the circuit.

a. Create a truth table according to FIGURE 1.

[4 marks]

AB AB A’ X=AB+A’
00 0 11
01 0 11
10 0 00
11 1 01

b. Boolean expressions can compare data of any type as long as both parts of the expression have
the same basic data type. State the output according to the input value given.
A = 1, B = 0 and C = 1
i. A’.B + C’(A+B)’
[1 mark]

0

ii. A+B’.A+C [1 mark]
[3 marks]
1
c. Draw a logic circuit based on the given expressions:

(̅̅ ̅ ̅̅+̅̅̅ ̅ ̅)̅. A

C

BY
A

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d. Write the Boolean expression based on FIGURE 2.

[3 marks]

Y= (AB) . (A’+B’)’

e. Draw a logic circuit that can best fit the description of the sentence below:

Nurul is only allowed by her father to go out to cinema with her brother, Ahmad.
However, they cannot go out if that day is raining.
[3 marks]

LEGEND:
A= Nurul
B= Ahmad
C= Day is raining
X= Go out to cinema

A

B

X

C

5. Logic diagrams are shows the wiring and connections of each individual logic gate that implements the
circuit.
a. Draw a logic circuit for = (̅(̅ ̅ ̅ ̅ ̅)̅̅+̅̅̅(̅ ̅ ̅̅. ̅ ̅̅ ̅))
[4 marks]

AB

BC’
C’

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b. Determine the output for each logic circuits: [2 marks]
i.

Y=0
ii.

Z=0 [2 marks]
[4 marks]
c. Draw a simple logic circuit
i. Z= (̅ ̅ ̅̅·̅ ̅̅ ) +C·D [3 marks]

A (AB)' Z
B CD (AB)' + CD
C
D

ii. Z= ( ̅̅ ̅̅·̅ ̅̅ ) ·C

A

B

(AB)' Z
C

C(AB)'

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6. Write a Boolean equation and logic circuit for each situation

i. Amran will watch a HBO movie if Opah comes along and it does not rain.

LOGIC CIRCUIT:

LEGEND:
W = Watch a HBO movie
O = Opah comes along
R = Rain
W= O . R’

ii. The entrance door will be automatically unlocked if the time is within office hours (0800-

1500), on a weekday (Monday-Friday) and it is not a public holiday.

LOGIC CIRCUIT:

LEGEND:
U= unlocked
T= Time
W= Weekday
H= Public holiday

U= W.T.H’

iii. Every participant must wear a red or yellow T-shirt, and a pair of dancing shoes to be

eligible for the competition, but miniskirts are not allowed.

LOGIC CIRCUIT:

LEGEND:
E= eligible for the competition

R= Red T-shirt
Y= Yellow T-shirt
S= wear dancing shoes
M=wear miniskirts
E= (R+Y) . S . M’

7. b. Determine a single logic gate to
replace the logic circuit below.
a. Determine a single logic gate to
replace the logic circuit below.

NOR NAND
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***NOTE:
1. A’.B’ ≠ (AB)’
2. A’+ B’ ≠ (A + B)’

c. Use a truth table to determine whether
TRUTH TABLE FOR 1:
TRUTH TABLE FOR 2:
CONCLUSION: ?

d. Complete the truth tables for these two Boolean expressions:

(a) Output = ( + + ̅ ) [4 marks]
[2 marks]
AB C AC A’ B+AC+A’ Output

00 =A(B+AC+A’)
00
01 0 01 1 0
01
10 1 01 1 0
10
11 0 01 1 0
11
1 01 1 0

0 00 0 0

1 10 1 1

0 00 1 1

1 10 1 1

8. Find the Boolean of Z, given that X is FALSE and Y is TRUE.

Z

FALSE

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(b) Draw a logic circuit and write a truth table for the following Boolean expression:
[4 marks]

P = Q’ + (Q. R)

R TRUTH TABLE:
Q
P
QR Q' + (Q.R)

Q'

(c) Form a valid Boolean expression from the following scenario:
[2 marks]

Good eating is not fill your plate more than once and then stand away from the food
table

LEGEND:
G : Group eating
P : Fill your plate
T : Stand away from the food table
G = P.T’

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