Download Lect5-CombinationalLogic

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CPS3340
COMPUTER ARCHITECTURE
Fall Semester, 2013
Lecture 5: Combinational Logic
Instructor: Ashraf Yaseen
09/10/2013
DEPARTMENT OF MATH & COMPUTER SCIENCE
CENTRAL STATE UNIVERSITY, WILBERFORCE, OH
Review

Last Class



Basic of Logic Design
This Class

Integrated Circuits

Decoder

Multiplexor

PLA

ROM

Don’t Care

Bus
Next Class

Design of ALU
Integrated Circuit

Integrated Circuit (IC)


A small electronic device made out of a semiconductor material
Classifications

SSI (small-scale integration)


MSI (medium-scale integration)


3,000~100,000 electronic components per chip
VLSI (very large-scale integration)


100~3,000 electronic components per chip
LSI (large-scale integration)


up to 100 electronic components per chip
100,0000 to 1,000,0000 electronic components per chip
ULSI (ultra large-scale integration)

More than 1 million electronic components per chip
Decoder

Decoder
logic block that has n-bit input and 2n outputs, where
only one output is asserted for each input combination
 If the input is i (in binary),
A
 then
output i is 1
 others are 0
Decoder Example

3-8 Decoder
Multiplexor

Multiplexor
A
selector
 The
output is selected by an input control
Implementation of a Multiplexor
n-input Multiplexor

A Multiplexor can have n-inputs
 Require

selective inputs
Implementation of an n-input Multiplexor
Two-level Logic


Try to Remember: Any Boolean Logic function can
be implemented with only NOT, AND, OR functions
We can also find that all logic functions can be
written in a canonical form, in 2 levels
 Sum
of Product
 Logical
 Product
Sum (OR) of terms joined by Product (AND)
of Sum
 Logical
Product (AND) of terms joined by Sum (OR)
Example

Consider a logic function

Equivalent to sum of products

Equivalent to product of sums
In Class Exercise

Considering the following truth table for D, write the
function of D using sum of products
Answer

Combinations that D is 1

Answer
Programmable Logic Array

Programmable Logic Array (PLA)
 Two
 An
stages of logic
array of AND gates (product terms)
 An array of OR gates
PLA Example

Considering the following table, implement the PLA
for D, E, F
PLA Example – cont.
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
A PLA can directly implement the truth table of a
set of logic functions with multiple inputs and
outputs.
 Each
entry where the output is true requires a product
term there will be a corresponding row in the PLA
 Each output corresponds to a potential row of OR gates
in the second stage
Another PLA Representation

Dot in the AND plane
 Input,
or its inverse, occurs in
the product term

Dot in the OR plane
 Corresponding
product term
appears in the corresponding
output
Read Only Memory

Read Only Memory (ROM)
Has a set of locations that can be read
 Contents of these locations are fixed


Programmable ROM (PROM)


Erasable Programmable Read Only Memory (EPROM)


Can be burnt using a device called a “ROM programmer”
Data in the ROM can be deleted under ultra-violet rays
EEPROM (Electrically Erasable Read Only Memory)

Data in the ROM can be erased by a simple electric current
ROM

Height
m
inputs
 2m addressable entries (input lines)

Width
n
outputs (functions)
 2n output bits

mxn is the shape of the ROM
ROMs and PLAs


PLA is partially decoded
ROM is fully decoded


Contains a full output word for every possible input combination
Always contain more entries than PLA
PLA (7 entries)
ROM (8 entries – 1 unused)
Don’t Care

Don’t Care
 We

don’t care about the actual values
Output Don’t Care
 We
don’t care about the value of an output for some
input combination

Input Don’t Care
 An

output only depends on some of the inputs
Advantages of Don’t Care
 Easier
to optimize the implementation of a logic
function
Example of Don’t Cares

Original Truth Table
Example of Don’t Cares

Output Don’t Cares

Input Don’t Cares
Array of Logic Elements

Bus
In logic design, a collection of
data lines that is treated
together as a single logical
signal
 Shared collection of lines with
multiple sources

32-bit wide 2-to-1 multiplexor
Summary

Integrated Circuits

Decoder

Multiplexor

PLA

ROM

Don’t Care

Bus
What I want you to do

Review Chapter 1