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Digital Circuits: Combinational Logic Components and Implementations, Study notes of Computer Science

Wellesley CollegeComputer Science

This document from the cs240 computer organization course at wellesley college explores various digital circuits, including decoders, encoders, multiplexers, demultiplexers, shifters, and programmable logic arrays (plas). Their functions, structures, and implementations using examples and diagrams.

Typology: Study notes

Pre 2010

Uploaded on 08/16/2009

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CS240 Computer Organization
Department of Computer Science
Wellesley College
Basic building blocks
Combinational circuits
Modular design
o In the old days, computers were constructed gate by gate.
Today the building blocks are somewhat larger.
Computer Hardware Complete Systems
Majors Blocks
Medium Scale Digital
Parts
Fundamental Elements
ALU, Controller,
I/O, Memory
Registers, Decoders,
Comparators, Counters, Clocks
Gates and Flip-Flops
Digital circuits 11-2
pf3
pf4
pf5
pf8
pf9

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CS240 Computer Organization

Department of Computer Science Wellesley College

Basic building blocks

Combinational circuits

Modular design

o In the old days, computers were constructed gate by gate.

Today the building blocks are somewhat larger.

Computer Hardware Complete Systems Majors Blocks Medium Scale Digital Parts Fundamental Elements ALU, Controller, I/O, Memory Registers, Decoders, Comparators, Counters, Clocks Gates and Flip-Flops Digital circuits 11-

Decoders

o The most common decoder

has an n-bit input and 2^ n

one-asserted outputs and is

implemented using code

detectors.

D 0

D 1

D 2

D 3

D 4

D 5

D 6

D 7

B 0

B 1

B^ B^2

0 B 1 B 2

D 0

D 1

D 7

... Digital circuits 11- Ta da! Digital circuits 11-

Steering circuits select select Multiplexer (^) Demultiplexer Digital circuits 11- Binary control

o Multiplexers generally

have 2^ n^ data inputs, one

data output, and n control

lines.

o Here’s the world’s

smallest Mux:

D 0

D 1

D 2

D 3

D 4

D 5

D 6

D 7

Mux F A B C Digital circuits 11-

Implementing Muxs with encoders Digital circuits 11- Muxs as combinational circuits

o A Mux and a voltage

source are all we need to

implement our old friend

the voting machine.

D 0

D 1

D 2

D 3

D 4

D 5

D 6

D 7

Mux F A B C Digital circuits 11-

Sum of products*

o A sum of products representation is the logical sum (OR)

of products (AND).

*Think of summing code detectors. Digital circuits 11- PLAs

o A programmable logic

array (PLA) has a set of

inputs and corresponding

input complements and

two stages of logic.

o The first state is an array

of AND gates which form

the product terms

(sometimes called

minterms).

o The second stage sums

the minterms.

Digital circuits 11-

For example,

o Here is our old friend. Recall D is logical OR, E checks for

exactly two 1s, and F is logical AND.

Digital circuits 11- PLA implementation Digital circuits 11-