1. طراحی مدارهای منطقی نیمسال دوم 92-93 دانشگاه آزاد اسلامی واحد پرند

2. طراحی مدارهای منطقی دانشگاه آزاد اسلامی واحد پرند جبر بول 2

3. 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

4. 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

5. Conversion of English Sentences to Boolean Equations  Examples (Without Truth Table) F = A. B Z = A.B’ + CD’

6. Conversion of English Sentences to Boolean Equations  Examples (With Truth Table)  f = 1 if N≥ 011 2 and  f = 0 if N < 011 2

7. Minterm and Maxterm Expansions  Minterms and Maxterms for Three Variables

8. Minterm and Maxterm Expansions  Standard (Canonical) SOP  Minterm Expansion  Standard (Canonical) POS  Maxterm Expansion

9. Minterm and Maxterm Expansions  Finding Minterm Expansion  Using X + X’ = 1

10. Minterm and Maxterm Expansions  Finding Maxterm Expansion  Using XX’ = 0

11. Minterm and Maxterm Expansions  Relation Between F and F’

12. 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

13. Incompletely Specified Boolean Functions  Don’t Care Minterms  Example  There is no output ABC=001 and 110

14. Examples of Truth Table Construction 1.1-bit binary adder  adds two 1-bit binary numbers

15. Examples of Truth Table Construction 2.2-bit binary adder  adds two 2-bit binary numbers

16. 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