程序代写代做代考 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
 One’s complement and two’s 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
DeMorgan’s
© 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: Demorgan’s 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
Let’s 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