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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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2749612

طراحی مدارهای منطقی

دانشگاه آزاد اسلامی واحد پرند

نیمسال دوم 92-93


2749612

طراحی مدارهای منطقی

دانشگاه آزاد اسلامی واحد پرند

جبر بول 2


Contents

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

Conversion of English Sentences to Boolean Equations

  • 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


Conversion of english sentences to boolean equations1

Conversion of English Sentences to Boolean Equations

  • Examples (Without Truth Table)

F = A . B

Z = A.B’ + CD’


Conversion of english sentences to boolean equations2

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

Minterm and Maxterm Expansions

  • Minterms and Maxterms for Three Variables


Minterm and maxterm expansions1

Minterm and Maxterm Expansions

  • Standard (Canonical) SOP  Minterm Expansion

  • Standard (Canonical) POS  Maxterm Expansion


Minterm and maxterm expansions2

Minterm and Maxterm Expansions

  • Finding Minterm Expansion

    • Using X + X’ = 1


Minterm and maxterm expansions3

Minterm and Maxterm Expansions

  • Finding Maxterm Expansion

    • Using XX’ = 0


Minterm and maxterm expansions4

Minterm and Maxterm Expansions

  • Relation Between F and F’


Incompletely specified boolean functions don t care minterms

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 minterms1

Incompletely Specified Boolean Functions  Don’t Care Minterms

  • Example

    • There is no output ABC=001 and 110


Examples of truth table construction

Examples of Truth Table Construction

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


Examples of truth table construction1

Examples of Truth Table Construction

  • 2-bit binary adder  adds two 2-bit binary numbers


Examples of truth table construction2

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


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