computing machinery chapter 3: combinational circuits

Computing Machinery

Chapter 3: Combinational Circuits

Half Adder

a b

s

c

HalfAdder

a b

c s

a b

s

c

HalfAdder

a b

c s

a b

s

c

a b

s

c

HalfAdder

a b

c s

HalfAdder

a b

c s

Full Adder

Full Adder Circuit

Simplifying the Full Adder Circuit

Cout = ab + acin + bcin

s = a b cin. ++

N-Bit Adder

Ripple-Carry Adder

gi = aibi

pi = ai + bi

ci+1 = gi + pici

Carry Look-Ahead Adder (CLA)

cinbiai

ith FA

sici+1

1. Will ith FA generate a carry bit?

2. Will ith FA propagate a carry bit?

3. What is the carry-out for the ith FA?

Carry-Out Bits Circuit for CLA

Four-Bit CLA Circuit

Cascading 4-Bit Adders to Make a 16-Bit Adder

Encoders

Building a 16 to 4 Encoder

Binary Coded Decimal (BCD) EncoderFunction Table

Encoders and Decoders

3-to-8 Decoder(aka 1-of-8)

Implementing a Boolean Function using an Decoder

F(x,y,z) = m( 1, 2, 5, 7 )

Multiplexers and Demultiplexers

4-to-1 Multiplexer

1-to-4 Demultiplexer

Implementing a Boolean Function using a Multiplexer

G(x,y,z) = m( 1, 4, 5, 6 )

Multiplexer as a Full-Adder

Magnitude Comparators

Designing a 2-Bit Magnitude Comparator

Voting Logic Circuit

Light Emitting Diode (LED) Displays

BCD to 7-Segment Display Function Table