Department of Electrical Engineering
McGill University
ECSE 221 Introduction to Computer Engineering
Assignment 2 – Combinational Logic
Question 1:
Due October 19
th
, 2009
A convenient shorthand for specifying truth tables is to list the set of minterms (or maxterms) for
which the corresponding Boolean function is true (or false).
Consider the following truth table:
A
B
C
D
F(A,B,C,D)
0
0
0
0
0
d
1
0
0
0
1
0
2
0
0
1
0
1
3
0
0
1
1
1
4
0
1
0
0
0
5
0
1
0
1
1
6
0
1
1
0
0
7
0
1
1
1
0
8
1
0
0
0
d
9
1
0
0
1
0
10
1
0
1
0
1
11
1
0
1
1
1
12
1
1
0
0
0
13
1
1
0
1
1
14
1
1
1
0
0
15
1
1
1
1
0
The shorthand for the sum-of-products (
∑∏
) and product-of-sums (
∏∑
) forms is shown at the
right of the truth table.
Given this specification for a Boolean function, answer the following
questions.
a)
Use algebraic methods to derive the minimal forms for both
∑∏
and
∏∑
assuming that don't
cares are set to 0 for
∑∏
and 1 for
∏∑
.
b)
Repeat the above using Karnaugh maps.
Here you may choose the don't cares to minimize
the resulting expressions.
c)
Repeat the minimization, this time assuming don't cares are all 0, using any minimization
method.
Prove algebraically that the resulting forms are equal (same truth table).
F
(
A
,
B
,
C
,
D
)
=
2,3, 5,10,11,13
+
1
∑
0,8
d
∑
F
(
A
,
B
,
C
,
D
)
=
1,4,6,7,9,12,14,15
+
0
∏
0,8
d
∏