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Computing Machinery Chapter 3: Combinational Circuits PowerPoint PPT Presentation


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Computing Machinery Chapter 3: Combinational Circuits. Half Adder. Full Adder. Full Adder Circuit. s = a b c in. +. +. Simplifying the Full Adder Circuit. C out = ab + ac in + bc in. N-Bit Adder. Ripple-Carry Adder. Carry Look-Ahead Adder (CLA). c in. a i. b i. g i = a i b i

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Computing Machinery Chapter 3: Combinational Circuits

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Computing machinery chapter 3 combinational circuits

Computing Machinery

Chapter 3: Combinational Circuits


Computing machinery chapter 3 combinational circuits

Half Adder


Computing machinery chapter 3 combinational circuits

Full Adder


Computing machinery chapter 3 combinational circuits

Full Adder Circuit


Computing machinery chapter 3 combinational circuits

s = a b cin.

+

+

Simplifying the Full Adder Circuit

Cout = ab + acin + bcin


Computing machinery chapter 3 combinational circuits

N-Bit Adder


Computing machinery chapter 3 combinational circuits

Ripple-Carry Adder


Computing machinery chapter 3 combinational circuits

Carry Look-Ahead Adder (CLA)

cin

ai

bi

gi = aibi

pi = ai + bi

ci+1 = gi + pici

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?

ith FA

ci+1

si


Computing machinery chapter 3 combinational circuits

Carry-Out Bits Circuit for CLA


Computing machinery chapter 3 combinational circuits

Four-Bit CLA Circuit


Computing machinery chapter 3 combinational circuits

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


Computing machinery chapter 3 combinational circuits

Encoders


Computing machinery chapter 3 combinational circuits

Building a 16 to 4 Encoder


Computing machinery chapter 3 combinational circuits

Binary Coded Decimal (BCD) Encoder

Function Table


Computing machinery chapter 3 combinational circuits

Encoders and Decoders


Computing machinery chapter 3 combinational circuits

3-to-8 Decoder

(aka 1-of-8)


Computing machinery chapter 3 combinational circuits

Implementing a Boolean Function using an Decoder

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


Computing machinery chapter 3 combinational circuits

Multiplexers and Demultiplexers


Computing machinery chapter 3 combinational circuits

4-to-1 Multiplexer


Computing machinery chapter 3 combinational circuits

1-to-4 Demultiplexer


Computing machinery chapter 3 combinational circuits

Implementing a Boolean Function using a Multiplexer

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


Computing machinery chapter 3 combinational circuits

Multiplexer as a Full-Adder


Computing machinery chapter 3 combinational circuits

Magnitude Comparators


Computing machinery chapter 3 combinational circuits

Designing a 2-Bit Magnitude Comparator


Computing machinery chapter 3 combinational circuits

Voting Logic Circuit


Computing machinery chapter 3 combinational circuits

Light Emitting Diode (LED) Displays


Computing machinery chapter 3 combinational circuits

BCD to 7-Segment Display Function Table


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