طراحی مدارهای منطقی
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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طراحی مدارهای منطقی
93-92نیمسال دوم
دانشگاه آزاد اسالمی واحد پرند
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دانشگاه آزاد اسالمی واحد پرندطراحی مدارهای منطقی
2جبر بول
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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
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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
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Conversion of English Sentences to Boolean Equations
Examples (Without Truth Table)
F = A . B
Z = A.B’ + CD’
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Conversion of English Sentences to Boolean Equations
Examples (With Truth Table)
f = 1 if N≥ 0112 and
f = 0 if N < 0112
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Minterm and Maxterm Expansions
Minterms and Maxterms for Three Variables
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Minterm and Maxterm Expansions
Standard (Canonical) SOP Minterm Expansion
Standard (Canonical) POS Maxterm Expansion
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Minterm and Maxterm Expansions
Finding Minterm Expansion Using X + X’ = 1
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Minterm and Maxterm Expansions
Finding Maxterm Expansion Using XX’ = 0
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Minterm and Maxterm Expansions
Relation Between F and F’
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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
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Incompletely Specified Boolean Functions Don’t Care Minterms
Example There is no output ABC=001 and 110
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Examples of Truth Table Construction
1. 1-bit binary adder adds two 1-bit binary numbers
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Examples of Truth Table Construction
2. 2-bit binary adder adds two 2-bit binary numbers
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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