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 All rights reserved.
Exclusive-OR Gate a) Gate Symbol, Boolean Equation a) Gate Symbol, Boolean Equation & Truth Table b) Timing Diagram
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 All rights reserved.
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
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.
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.
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
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
SAMPLE EXAM QUESTIONS
K-Map with “Don’t Care” Conditions Input Output Example : 3 variables with output “don’t care (X)”
K-Map with “Don’t Care” Conditions (cont’d) 4 variables with output “don’t care (X)”
“Don’t Care” Conditions Example: Determine the minimal SOP using K-Map: Answer: Answer: K-Map with “Don’t Care” Conditions (cont’d)
Solution : AB CD X 1 0 X X Minimum SOP expression is CD AD BC