Gates and Circuits

Three Main Gates

AND OR NOT

NAND Gates

NOT AND

TFF

TTF

TFT

FTT

A NAND BBA

Gate Diagrams

Example: MR + S

Gate Diagrams

Example:

Gate Diagrams

Example: (MR + S) (RS)’

Gate Diagrams

Exercise:

Truth Table (to Expression) to Gates

First, build the Boolean algebra expression that gives Z Z = AB + A’B’

TFF

FTF

FFT

TTT

ZBA

Truth Table to Gates

Z = AB + A’B’ Next, build the

circuit that goes with the Boolean algebra expression Z

TFF

FTF

FFT

TTT

ZBA

Z = AB + A’B’

Boolean Expression to Gates

Exercise: (A + B’) A

Boolean Expression to Gates

Exercise: (A + B’) A

Multi-input AND and OR

What circuit corresponds to ABC? A+B+C?

Binary Addition

The first step in building our computer…

Binary Addition

TrueFalseFalseFalse

FalseTrueTrueFalse

10110

+ 1+ 0+ 1+ 0

1100

Sum

Carry

Binary Addition

000

010

001

111

CarryBA

000

110

101

011

SumBA

Sum Circuit

000

110

101

011

SumBA

Sum = AB’ + A’B

Carry Circuit

000

010

001

111

CarryBA

Carry = AB

Half Adder - Sum and Carry

Full Adder

4 Bit Adder

Computers represent numbers in parallel.

Exercises

Give Boolean expressions and construct circuits with the following properties (using AND, OR or NOT gates):

Exercises

A) B)

100

110

101

011

ZBA

0000

1100

1010

0110

1001

0101

0011

1111

ZCBA

Exercises

2 - Fill in a truth table and give a Boolean expression for the following circuit.