Princess Nora Bint Abdulrahman University CS121- Digital Logic DesignFaculty of Computer and Information Sciences Second Semester 1433/1434HDepartment of the Computer Sciences Homework -3 (Chapter 3)
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Q1. Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions.
a. F=∑XYZ
(1,3,5,6,7)
b. F= ∏W ,X ,Y
(1,4,5,6,7)
c. F= ∏A, B, C , D
(4,5,6,13,15)
Q2. Simplify the following Boolean functions by first finding the essential prime implicants.
a. F ( A , B ,C )=∑ (0,1,2,4)
b. F (W , X ,Y ,Z )=∏ (1,2,4,7,8,11,13,14 )
Q3.Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions, together with the don’t-care conditions d.
a. F= ∑W , X ,Y , Z
(0,1,3,5,14)+d (8,15)
b. F= ∑A, B, C , D
( 4,6,7,9,13 )+d (12)
Q4. implement the following Boolean function F, using the two level forms:
F ( A , B ,C ,D )=∑ (0,1,2,3,4,8,9,12)
a. NAND-NANDb. NOR-NOR
Q5. An Exclusive NOR (XNOR) gate is a 2-input gate whose output is 1 if both of the inputs are the same. Write a truth table, sum-of-products expression, and corresponding NOR circuit for the XNOR function.
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