CPS3340 COMPUTER

ARCHITECTURE Fall Semester, 2013

CPS3340 COMPUTER

ARCHITECTURE Fall Semester, 2013

09/10/2013

Lecture 5: Combinational Logic

Instructor: Ashraf YaseenDEPARTMENT OF MATH & COMPUTER SCIENCECENTRAL STATE UNIVERSITY, WILBERFORCE, OH

1

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)

up to 100 electronic components per chip MSI (medium-scale integration)

100~3,000 electronic components per chip LSI (large-scale integration)

3,000~100,000 electronic components per chip VLSI (very large-scale integration)

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 A 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), 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 Sum (OR) of terms joined by Product (AND) Product 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 stages of logic

An 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.

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

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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) Can be burnt using a device called a “ROM programmer”

Erasable Programmable Read Only Memory (EPROM) 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