Department of Electrical and Computer Engineering
ECSE 221 – Introduction to Computer Engineering 1
Assignment 2 – Combinational Logic
Due: Monday, February 11
th
2008, 5:00 pm
Question 1
Consider the truth table for the function X = f(A,B,C,D) shown below.
A B C D X
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
a)
Using the Karnaugh Map method, determine the minimal canonical forms (i.e.
∑π
and
π∑
respectively) corresponding to the truth table shown above.
List any multiple
solutions.
Repeat the analysis using algebraic manipulation for each of the solutions you
obtained.
b)
Using algebraic manipulation, prove the equivalence of the
∑π
and
π∑
forms obtained.
c)
Suppose that term #15 was set to d, i.e.,
don’t care
.
Determine the resulting minimal
canonical forms using the minimization method of your choice.
Using algebraic
manipulation, prove that the resulting forms are equal.
Question 2
In this question you will build implementations for each of the solutions you obtained in
Question 1a using a variety of technologies.
The LogicWorks simulator, available on all
Engineering machines, will be used for this exercise.
(Unfortunately LogicWorks is licensed
software, so you will have to purchase your own copy if you wish to use it on your personal
A shorthand notation for specifying truth tables is to list the
minterm of maxterm numbers corresponding to the function’s
1’s or 0’s respectively using the following notation,
X
"#
=
{3,4,6,7,11,12,14}
A
,
B
,
C
,
D
$
,
X
#"
=
{0,1,2,5,8,9,10,13,15},
A
,
B
,
C
,
D
%
where X
∑π
corresponds to the Sum of Products form, and X
π∑
corresponds to the Product of Sums form.
Note: the number associated with a minterm or maxterm is
simply the binary value associated with the input, A,B,C,D.
For example, the minterm corresponding to A,B,C,D=0,1,1,1
is minterm 7.
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