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

Conversion of English Sentences to Boolean Equations

Examples (Without Truth Table)

F = A . B

Z = A.B’ + CD’

Conversion of English Sentences to Boolean Equations

Examples (With Truth Table)

f = 1 if N≥ 0112 and

f = 0 if N < 0112

Minterm and Maxterm Expansions

Minterms and Maxterms for Three Variables

Minterm and Maxterm Expansions

Standard (Canonical) SOP Minterm Expansion

Standard (Canonical) POS Maxterm Expansion

Minterm and Maxterm Expansions

Finding Minterm Expansion Using X + X’ = 1

Minterm and Maxterm Expansions

Finding Maxterm Expansion Using XX’ = 0

Minterm and Maxterm Expansions

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

Examples of Truth Table Construction

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

Examples of Truth Table Construction

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

Examples of Truth Table Construction

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