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1007ICT / 1807ICT / 7611ICT Computer Systems & Networks
3A. Digital Logic and Digital Circuits

Last Section: Data Representation

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Topics Covered:
 Representing binary integers
 Conversion from binary to decimal
 Hexadecimal and octal representations
 Binary number operations
 One’s complement and two’s complement
 Representing characters, images and audio

Lecture Content
 Learningobjectives
 Digitallogic,Basiclogicgates,Booleanalgebra  Combinatoriallogicgates
© . Revised and updated by , , and Wee Lum 3

Learning Objectives
At the end of this lecture you will have:
 Gained an understanding of basic logic gates
 Learnt the truth tables associated with the basic logic gates
 Gained an understanding of combinatorial logic gates
 Learnt the truth tables associated with combinatorial logic gates
© . Revised and updated by , , and Wee Lum 4

Digital Logic (Section 2.2)
All digital computers are built from a set of low
Logic Gates.
level digital logic switches or
Gates operate on binary signals that only have one of two values:
 Signalsfrom0to2voltsisusedtorepresentabinary0(OFF)  Signalsfrom3to5voltsisusedtorepresentabinary1(ON)  Signals between 2 and 3 volts represent an invalid state
Three basic logic functions that can be applied to binary signals:
More complex functions can be built from these three basic gates
 AND:  OR:  NOT:
outputtrueifALLinputsaretrue outputtrueifANYinputistrue outputistheinverseoftheinput
© . Revised and updated by , , and Wee Lum 5

Basic Logic Gates (Section 2.4)
Boolean expression
Truth Table
x = a AND b
x = a OR b
© . Revised and updated by , , and Wee Lum 6

Boolean Algebra
There is a basic set of rules about combining simple binary functions.
x OR 0 = x x OR 1 = 1 x OR x = x x OR x = 1 (x)=x
xAND0 = 0 xAND1 = x xANDx = x xANDx = 0
© . Revised and updated by , , and Wee Lum 7

Combinatorial Logic Gates
Next Slide
Symbol Equivalent
Boolean expression
Truth Table
© . Revised and updated by , , and Wee Lum 8
x = a AND b x = a OR b x = a XOR b

Boolean Algebra – 2
 This second set of rules are more powerful. OR – form AND – form
(xORy) = xANDy
(xANDy) = xORy
OR – form AND – form
NAND = Theorem
DeMorgan’s
© . Revised and updated by , , and Wee Lum 9

The eXclusive-OR Gate (XOR)
Looking at the truth table we see that the XOR function can be described as:
 x = (aANDb)OR(aANDb)  x=aXORb
 This function can be built in 3 ways: Demorgan’s Theorem
aaa bbb aaa bbb
x = (aANDb)OR(aANDb) x = (aANDb)OR (aANDb) x = (aANDb)AND(aANDb)
© . Revised and updated by , , and Wee Lum 10

© . Revised and updated by , , and Wee Lum 11

Logic Unit
Let’s try to create a “programmable” logic unit that permits us to apply a predefined logic function to a given set of inputs.
Output Select
We need a function that lets us select what operation to perform
AND OR XOR
© . Revised and updated by , , and Wee Lum 12

Have considered:
 Operation of basic logic gates
 Combinatorial logic gates, Truth tables
© . Revised and updated by , , and Wee Lum 13

 Logic unit, Selection logic, Decoder logic
 Multiplexing and demultiplexing
© . Revised and updated by , , and Wee Lum 14

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