Chapter 1 CSC159

Digital System
and Logic

CSC159 – Computer Organization

Lesson Outcomes

 Boolean Algebra AND OR
NOT XOR
 Boolean Operations

 Logic Gates

 Truth Tables

 Combinational Logic Circuits

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Integrated Circuits (ICs)

 The building blocks of computers

 “An IC is a small chip that can function as an amplifier, oscillator,
timer, microprocessor, or even computer memory. Usually made of
silicon and can hold anywhere from hundreds to millions of
transistors, resistors, and capacitors.”

 Designed for specialized functions

 Examples: the CPU, bus interface, memory
management unit

 Transistors  commonly used in digital circuits as

electronic switches which can be either in an "on" or
"off" state

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Boolean Algebra

 The digital computer is based on Boolean algebra

 Describes rules that govern constants & variables that can
take on two values (Boolean logic)

 Can be represented in many ways:

 true or false, on or off, yes or no, 1 or 0, light or dark…

 Transistors: means for implementing Boolean algebra

 Switches: on/off to represent the 0’s and 1’s of binary digital
circuits

 Combined to form logic gates

 Boolean logic rules can be described as formulas, or
by a truth table

 Specifies the result for all possible combinations of inputs

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Boolean Operations

 3 fundamental operations: AND, OR, NOT …
XOR

Operation Symbol Equation
AND • C=A•B
OR (INCLUSIVE-OR) + C=A+B
NOT ˉ C=Ā
XOR (EXCLUSIVE-OR) ⊕ C=A⊕B

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AND Operation

 The result of an AND operation is TRUE if and
only if both (or all) input operands are TRUE

Truth table:(2-input) 22 = 4 AND gate:

ABC C
000
010
100
111

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OR Operation

 The result of an OR operation is TRUE if the
values of any (one or more) of the input
operands are TRUE

Truth table: OR gate:

ABC C
000
011
101
111

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NOT Operation

 The result of a NOT operation is TRUE if and
only if the single is FALSE

 The result is always the opposite state from the input
operand

Truth table:(1-input) NOT gate:

21 = 2

AC

01 A C
10

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XOR Operation

 The result of an XOR operation is TRUE if
either A or B is TRUE but not both

 Gives a true output when the number of true
inputs is odd

Truth table: XOR gate:

ABC

000 C
011

101

11 0 9

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Truth Table (3-input) 23 = 8

ABC Y
000
001 10
010
011
100
101
110
111

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Truth Table (4-input)

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Combinational Logic Circuits

 Combinational Logic Circuits are made up
from basic logic gates that are “combined” or
connected together to produce more
complicated switching circuits.

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