[SOLVED] 1007ICT / 1807ICT / 7611ICT Computer Systems & Networks

1007ICT / 1807ICT / 7611ICT Computer Systems & Networks
3A. Digital Logic and Digital Circuits
Dr. Sven Venema Dr. Vallipuram Muthukkumarasamy

Last Section: Data Representation
Topics Covered:
Representing binary integers
Conversion from binary to decimal
Hexadecimal and octal representations
Binary number operations
Ones complement and twos complement
Representing characters, images and audio

Lecture Content
Learningobjectives
Digitallogic,Basiclogicgates,Booleanalgebra Combinatoriallogicgates
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 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
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 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
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 5

Basic Logic Gates (Section 2.4)
Name
Symbol
Boolean expression
Truth Table
a b
AND
x
AND
a b
OR
x
OR
NOT
a NOT x
x = a AND b
x = a OR b
x=a
A
X
0
1
1
0
A
B
X
0
0
0
0
1
0
1
0
0
1
1
1
A
B
X
0
0
0
0
1
1
1
0
1
1
1
1
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 6

Boolean Algebra
There is a basic set of rules about combining simple binary functions.
OR AND

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
aaa
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 7

Name
Symbol Equivalent
Boolean expression
Truth Table
XOR
x
Combinatorial Logic Gates
a b
Next Slide
A
B
X
0
0
1
0
1
1
1
0
1
1
1
0
A
B
X
0
0
1
0
1
0
1
0
0
1
1
0
A
B
X
0
0
0
0
1
1
1
0
1
1
1
0
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 8
NAND
NOR
XOR
a b
NAND
x
a b
NOR
x
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
NOR =
NAND = Theorem
DeMorgans
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 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: Demorgans Theorem
aaa bbb aaa bbb
XOR

A
B
X
0
0
0
0
1
1
1
0
1
1
1
0
x = (aANDb)OR(aANDb) x = (aANDb)OR (aANDb) x = (aANDb)AND(aANDb)
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 10

Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 11

Logic Unit
Lets try to create a programmable logic unit that permits us to apply a predefined logic function to a given set of inputs.
ab
Output Select
We need a function that lets us select what operation to perform

AND OR XOR
NOT

Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 12

Summary
Have considered:
Operation of basic logic gates
Combinatorial logic gates, Truth tables
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 13

Next.
Logic unit, Selection logic, Decoder logic
Multiplexing and demultiplexing
Ruben Gonzalez. Revised and updated by Sven Venema, Vallipuram Muthukkumarasamy, and Wee Lum Tan
Page 14