Princess Nora University
College of Computer and Information Sciences
Department of Computer Sciences
CS 121- Digital Logic Design
2 nd Semester 1433-1434H
Homework -3 ( Chapter 3 )
Model Answer
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) x yz
1
1
1
1 1
F = z + xy b. 𝐹 = ∏
𝑊,𝑋,𝑌
(1,4,5,6,7)
F (w,x,y) = ∑(0,2,3) w xy
1 1 1
F = w'y' + w'x c. 𝐹 = ∏
𝐴,𝐵,𝐶,𝐷
(4,5,6,13,15)
F(a,b,c,d) = ∑(0,1,2,3,7,8,9,10,11,12,14) ab cd
1
1
1
1
1
1
1
1
1
1
1
F = b' + ad' + a'cd
Q2. Simplify the following Boolean functions by first finding the essential prime implicants. a. 𝐹(𝐴, 𝐵, 𝐶) = ∑(0,1,2,4) a bc
1
1
1 1
F = a'b' + b'c' + a'c', All are essentials.
b. 𝐹(𝑊, 𝑋, 𝑌, 𝑍) = ∏(1,2,4,7,8,11,13,14) wx yz
1
1
1
1
1
1
1
1

No possible simplification, all function minterms are essentials.
F = w'x'y'z' + w'x'yz + w'xy'z + w'xyz' + wx'y'z + wx'yz' + wxy'z' + wxyz
Q.3 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) wx yz
1 x
1
1
1 x
1
F = x'y'z' + w'y'z + w'x'z + wxy b. 𝐹 = ∑
𝐴,𝐵,𝐶,𝐷
(4,6,7,9,13) + 𝑑(12) ab cd
1 x
1
1
1 1
F = bc'd' + a'bc + ac'd
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-NAND ab cd
1
1
1
1
1
1
1 1
F = c'd' + b'c' + a'b'


b.
NOR-NOR ab cd
0
0
F' = bc + bd + ac
F = (b'+c') (b'+d') (a'+c')
0
0
0
0
0
0

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 .
Truth table:
Sum of product experresion:
A XNOR B = A'B' + AB
XNOR circuit using NOR: