1. Figure 5–5 Exclusive-OR logic diagram and symbols. Open file F05-05 to verify the operation. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

2. Exclusive-OR Gate a) Gate Symbol, Boolean Equation a) Gate Symbol, Boolean Equation & Truth Table b) Timing Diagram

3. Figure 5–6 Two equivalent ways of implementing the exclusive-NOR. Open file F05-06 to verify the operation. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

4. Standard Forms of Boolean Expressions 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

5. Standard Forms of Boolean Expressions 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.

6. Standard Forms of Boolean Expressions 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.

7. Standard Forms of Boolean Expressions 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

8. Standard Forms of Boolean Expressions 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

9. SAMPLE EXAM QUESTIONS

10. K-Map with “Don’t Care” Conditions Input Output Example : 3 variables with output “don’t care (X)”

11. K-Map with “Don’t Care” Conditions (cont’d) 4 variables with output “don’t care (X)”

12. “Don’t Care” Conditions  Example: Determine the minimal SOP using K-Map: Answer: Answer: K-Map with “Don’t Care” Conditions (cont’d)

13. Solution : 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