CPSC 3300 - Spring 2017
Homework 3
Due at class time on Thursday, Feb. 9
1. Consider A*( (~A) + B ) = A*B. Show by truth table that this is true.
(10 pts.)
A B | ~A | ~A + B | A*(~A+B) | A*B
-----------+--------+------------+--------------+---------
2. Given a 2-to-1 mux, an input line A, true line 1 (i.e., Vcc), and
false line 0 (i.e., Gnd), show how you can construct the equivalent
of a NOT gate to produce ~A. (10 pts.)
3. Given a 4-to-1 mux, input lines A and B, true line 1 (i.e., Vcc), and
false line 0 (i.e., Gnd), show how you can construct the equivalent
of an OR gate to produce A+B. (10 pts.)
4. Given a 4-to-1 mux, input lines A and B, true line 1 (i.e., Vcc), and
false line 0 (i.e., Gnd), show how you can construct the equivalent
of an AND gate to produce A*B. (10 pts.)
5. Simplify the following Karnaugh maps for functions D, E, and F.
(x is don't care) (10 pts. each)
D \ BC
A \ 00 01 11 10
+----+----+----+----+
0 | 1 | 0 | 0 | 1 | D = fn(A,B,C) = ____________________
+----+----+----+----+
1 | 0 | 0 | 1 | 1 |
+----+----+----+----+
E \ BC
A \ 00 01 11 10
+----+----+----+----+
0 | 1 | x | 0 | x | E = fn(A,B,C) = ____________________
+----+----+----+----+
1 | 1 | 0 | 0 | 1 |
+----+----+----+----+
F \ CD
AB \ 00 01 11 10
+----+----+----+----+
00 | 0 | 1 | 1 | 0 | F = fn(A,B,C,D) = ____________________
+----+----+----+----+
01 | 0 | 1 | 0 | 0 |
+----+----+----+----+
11 | 1 | 1 | 0 | 0 |
+----+----+----+----+
10 | 1 | 1 | 1 | 0 |
+----+----+----+----+
6. Consider a function F to compare two two-bit fields, x1 x0 and y1 y0,
and produce a one on output only if the two fields are the same.
(10 pts. each)
(a) Write a simplified SOP logic function using only AND, OR, NOT
operators to implement the two-bit comparison.
(b) Draw the circuit using AND, OR, and NOT gates to implement the
function. (In your diagram, you can choose to represent inverted
values as inputs with open circles on the AND and OR gates
instead of using explicit NOT gates.)
(c) Draw a PLA implementation of the circuit in the style of the
final diagram of
www.cs.umd.edu/class/spring2003/cmsc311/Notes/Comb/pla.html