Winter 2009
ENGR 160 – DIGITAL CIRCUITS
Department of Engineering & Design at Eastern Washington University
HOMEWORK #4
DUE: February 5, 2009
NOTE: This is true for any homework, but specially for this one: Make sure you do things neatly, as it will help
you a lot in working out these k-map problems.
1. (10 pts) Given the function P(A, B, C) =
(0, 2, 5),
a. Express P in both canonical forms.
b. Show the circuit diagram of simplified P using AND, OR, and NOT gates.
c. Show the circuit diagram of simplified P using AND and NOT gates only.
d. Show the circuit diagram of simplified P in OR and NOT gates only.
2. (10 pts) Given
P(A, B, C) =
(0, 1, 3, 5)
Q(A, B, C) =
(1, 4, 5, 7)
Find
i) P’ in sum of minterms form.
ii) P’ in product of maxterms form.
iii) P’Q in sum of minterms form.
iv) P’ + Q in product of maxterms form.
3. (10 pts) Find the minimum SOP and POS for each of the following functions using K-maps:
a. F = (0, 2, 3, 4, 6)
b. F = Π(0, 1, 4)
4. (70 pts) For each of the functions below, write a truth table (neatly!!) and simplify to a SOP form using k-maps.
i) F(A, B, C) = (A + B’)C’ + A’C
ii) F(X, Y, Z) = (X + Y’)(X’ + Z) + ZY’
iii) F(A, B, C, D) = AB’C + A’BC’D + A’BCD’ + B’D’
iv) F(W, X, Y, Z) = WX’ + Z’(Y’ + W’) + W’Z’Y’
v) F(P, Q, R, S) = PQ’(R’S’ + P’Q’)RS’ + (P + QR)’SR’
vi) F(A, B, C) = A’BC’ + (ABC)’ + AB’(C’ + B’)
vii) F(W, X, Y, Z) = W’X’(Y’ + Z’W’) + (XYW)’(X’ + W’X’) + (X’ + Y’)