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طراحی مدارهای منطقی. دانشگاه آزاد اسلامی واحد پرند. نیمسال دوم 92-93. طراحی مدارهای منطقی. دانشگاه آزاد اسلامی واحد پرند. جبر بول 2 . Contents. Combinational Logic Design Conversion of English Sentences to Boolean Equations Using a Truth Table Minterm and Maxterm Expansions

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### طراحی مدارهای منطقی

دانشگاه آزاد اسلامی واحد پرند

نیمسال دوم 92-93

### طراحی مدارهای منطقی

دانشگاه آزاد اسلامی واحد پرند

جبر بول 2

• 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

• The three main steps in designing a single-output combinational switching circuit are

• Find a switching function that specifies the desired behavior of the circuit

• With or Without Truth Table

• Find a simplified algebraic expression for the function

• 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

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

• 1-bit binary adder  adds two 1-bit binary numbers

• 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