1. School of Computer and Communication Engineering, UniMAP DKT 122/3 - DIGITAL SYSTEM I Chapter 4A:Boolean Algebra and Logic Simplification) Mohd ridzuan mohd nor mohdridzuan@unimap.edu.my 019-3806067 1

2. School of Computer and Communication Engineering, UniMAP Outline  Standard Forms of Boolean Expressions  Boolean Operations & expression  Laws & rules of Boolean algebra  DeMorgan’s Theorems  Boolean analysis of logic circuits  Simplification using Boolean Algebra  Standard forms of Boolean Expressions  Boolean Expressions & truth tables  The Karnaugh Map  Karnaugh Map SOP minimization  Karnaugh Map POS minimization  5 Variable K-Map  Programmable Logic 2

3. School of Computer and Communication Engineering, UniMAP Standard Forms of Boolean Expressions 3 Sum of Products (SOP) Products of Sum (POS) Notes:  SOP and POS expression cannot have more than one variable combined in a term with an inversion bar  There’s no parentheses in the expression

4. School of Computer and Communication Engineering, UniMAP Standard Forms of Boolean Expressions 4 Converting SOP to Truth Table  Examine each of the products to determine where the product is equal to a 1.  Set the remaining row outputs to 0.

5. School of Computer and Communication Engineering, UniMAP Standard Forms of Boolean Expressions 5 Converting POS to Truth Table  Opposite process from the SOP expressions.  Each sum term results in a 0.  Set the remaining row outputs to 1.

6. Standard Forms of Boolean Expressions 6 The standard SOP Expression  All variables appear in each product term.  Each of the product term in the expression is called as minterm.  Example:  In compact form, f(A,B,C) may be written as

7. School of Computer and Communication Engineering, UniMAP Standard Forms of Boolean Expressions 7 The standard POS Expression  All variables appear in each product term.  Each of the product term in the expression is called as maxterm.  Example:  In compact form, f(A,B,C) may be written as

8. School of Computer and Communication Engineering, UniMAP K-Map with “Don’t Care” Conditions 8 Input Output Example : 3 variables with output “don’t care (X)”

9. School of Computer and Communication Engineering, UniMAP K-Map with “Don’t Care” Conditions (cont’d) 9 4 variables with output “don’t care (X)”

10. School of Computer and Communication Engineering, UniMAP “Don’t Care” Conditions  Example: Determine the minimal SOP using K-Map: Answer: Answer: 10 K-Map with “Don’t Care” Conditions (cont’d)

11. School of Computer and Communication Engineering, UniMAP Solution : 11 AB CD 00 01 11 10 00 01 11 10 0 1 1 0 1 X 1 0 X X 0 0 1 0 0 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10 Minimum SOP expression is CD AD BC

12. School of Computer and Communication Engineering, UniMAP Q & A 12