CPSC 3300 - Spring 2016
Homework 3
Due at class time on Monday, Feb. 8
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. Give the simplified logic expressions for outputs S0 and S1 in the
following abbreviated truth table for a 4-to-2 priority encoder.
(15 pts. each)
in0 in1 in2 in3 | S0 S1 E
----------------+---------
0 0 0 0 | x x 1
0 0 0 1 | 1 1 0
0 0 1 x | 1 0 0
0 1 x x | 0 1 0
1 x x x | 0 0 0