ECE 349 Homework Assignment #2
1. Find an expression for f=a0b0c0+abc0+a0bc +ab0cthat uses only the exclusive-OR
and complement operations.
2. The following table shows the input and output voltages for a 2-input logic gate circuit.
Translate the table to a truth table using positive logic and then negative logic. What
are the logic functions realized in each case?
e1e2e0
0 0 0
0 +5 +5
+5 0 +5
+5 +5 +5
3. Express each of the following as minterm expansions.
(a) f(a, b, c) = a+b0c(b) f(x, y, z ) = QM(0,4,5,7)
4. Express each of the following as maxterm expansions.
(a) f(a, b, c) = (a+b0)(a0+b+c)(b+c0) (b) f(x, y, z) = Pm(1,3,5,6)
5. For f(a, b, c) = (ab+c)(a0+b0), find the minterm and maxterm expansions (use mand
Mnotation).
6. For the table below, express f as a minterm expansion (use mnotation) and as a
maxterm expansion (use Mnotation).
a b c f
0 0 0 0
0 0 1 1
0 1 0 X
0 1 1 1
1 0 0 0
1 0 1 X
1 1 0 1
1 1 1 0
7. For the truth table of the previous problem, find the simplest expression for f.
8. A bank vault has three locks with a different key for each lock. Each key is owned by a
different person. In order to open the door, at least two people must insert their keys
into the assigned locks. The signals A,B, and Care 1 if there is a key inserted into
lock 1, 2, or 3, respectively. Write an equation for the variable Z, which is 1 iff the
door should open.
