Published on 20 Apr 2013

Department

Computer Science

Course

CSC258H1

Professor

LOGIC DEVICES

Building up from gates

o Some common and more complex structures

Multiplexers (MUX)

Adders (half and full)

Subtractors

Comparators

Decoders

Seven-segment decoders

o Certain structures are common to many circuits, and have block

elements of their own

Karnaught map review – moved to jan18ce

Multiplexers (MUX)

o Behavior:

output is X if S = 0; otherwise output is Y if S = 1

o Multiplexer design

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Adders

o Also known as binary adders

Small circuits devices that add two digits together

Combind together to create interative combinational circuits

o Types of adders

Half Adders (HA)

Like an OXR for sum (s) and AND for carry (c)

Full Adders (FA)

Ripple Carry Adder

Carry-Look-Ahead Adder (CLA)

o Binary Math review

Each digit of a demical number represents a power of 10:

258 = 2*102 + 5*101 x+ 8*100

Each digit of a binary number represents a power of 2:

011012 = 0*24 + 1*23 + 1*22 + 0*21 + 1*20

= 1310

Binary Addition example

27 + 53 95 + 181

27 = 00011011 95 = 01011111

53 = 00110101 181 = 10110101

o Half Adders

A 2-input, 1-bit width binary adder that performs the following

computations:

A half adder adds two bits to produce a two-bit sum

The sum is expressed as a sum bit S and a carry bit C

Half Adder Implementation

Equations and circuits for half adder units are easy to

define (even w/o k-maps)

o Full Adders

Similar to half-adders, but with another input Z, which

represents a carry-in bit

C and Z are sometimes labels as Cout and Cin

When Z is 0, the unit behaves exactly like a half adder

When Z is 1, the full adder performs the following computations

Full Adder Design

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Then let carry generate

And let carry propagate

Resultant circuit

o Ripple-Carry Binary Adder

Full adder units chained together in order to perform operations

on singal vectors

o The role of Cin

Why can’t we judt have a half-adder for the smallest (right-

most) bit?

We could, if we were only interested in addition. But the last bit

allows use to do subtraction as well.

## Document Summary

Building up from gates: half adders. A 2-input, 1-bit width binary adder that performs the following: some common and more complex structures computations: Seven-segment decoders: certain structures are common to many circuits, and have block elements of their own. Karnaught map review moved to jan18ce. Output is x if s = 0; otherwise output is y if s = 1. A half adder adds two bits to produce a two-bit sum. The sum is expressed as a sum bit s and a carry bit c. Equations and circuits for half adder units are easy to define (even w/o k-maps: full adders. Similar to half-adders, but with another input z, which. C and z are sometimes labels as cout and cin. When z is 0, the unit behaves exactly like a half adder. When z is 1, the full adder performs the following computations: multiplexer design. Adders: also known as binary adders. Small circuits devices that add two digits together.