طراحی مدارهای منطقی

طراحی مدارهای منطقی

93-92نیمسال دوم

دانشگاه آزاد اسالمی واحد پرند

دانشگاه آزاد اسالمی واحد پرندطراحی مدارهای منطقی

2جبر بول

Contents

Combinational Logic Design

Conversion of English Sentences to Boolean

Equations

Using a Truth Table

Minterm and Maxterm Expansions

Incompletely Specified Functions

Examples of Truth Table Construction

Conversion of English Sentences to Boolean Equations

The three main steps in designing a single-output

combinational switching circuit are

1. Find a switching function that specifies the desired

behavior of the circuit• With or Without Truth Table

2. Find a simplified algebraic expression for the

function

3. Realize the simplified function using available logic

element


Examples (Without Truth Table)

F = A . B

Z = A.B’ + CD’


Examples (With Truth Table)

f = 1 if N≥ 0112 and

f = 0 if N < 0112


Minterms and Maxterms for Three Variables


Standard (Canonical) SOP Minterm Expansion

Standard (Canonical) POS Maxterm Expansion


Finding Minterm Expansion Using X + X’ = 1


Finding Maxterm Expansion Using XX’ = 0


Relation Between F and F’

Incompletely Specified Boolean Functions Don’t Care Minterms

Example There is no output ABC=001 and 110

• Both 0

• First 1, Second 0

• Both 1

Incompletely Specified Boolean Functions Don’t Care Minterms

Example There is no output ABC=001 and 110


1. 1-bit binary adder adds two 1-bit binary numbers


2. 2-bit binary adder adds two 2-bit binary numbers


Input (A, B, C, D) represent 8-4-2-1 binary-coded-decimal digit.

Output (Z) is 1 iff the decimal number represented by the inputs is exactly divisible by 3. Only valid BCD digits occur as inputs.

0 0000 3 0011 6 0110 9 1001

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