Computing Machinery Chapter 3: Combinational Circuits.

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Presentation transcript:

Computing Machinery Chapter 3: Combinational Circuits

Half Adder

Full Adder

Full Adder Circuit

Simplifying the Full Adder Circuit C out = ab + ac in + bc in s = a b c in. + +

N-Bit Adder

Ripple-Carry Adder

g i = a i b i p i = a i + b i c i+1 = g i + p i c i Carry Look-Ahead Adder (CLA) c in bibi aiai ith FA sisi c i+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) Encoder Function 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