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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