ECE2022
HWK 3
D07
Homework is due Tuesday April 3, 2006.
Problem 1 – 30 points
We will design part of a set of logic circuits that tests numbers for divisbility for certain prime
numbers as part of an information encryption system.
The binary number
A
is represented by a
four bit unsigned number:
A
= (
a
3
, a
2
, a
1
, a
0
) where
a
0
is the least signiFcant bit, etc. The circuit
you must design will have a single output,
F
, which must take on the value of 1 if
A
is divisible by
2 or 3 and zero otherwise, except when
A
= 0 (which is “technically” divisible by any number) for
which case we want
F
= 0.
(a)
Give the truth table for
F
as a function of
a
3
, a
2
, a
1
, a
0
.
(b)
Write out the canonical sum of minterms expression for
F
.
f
0
=
1
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Obtain a simplifed expression For
F
using a Karnaugh Map. (Be sure to show the Karnaugh
map and the prime implicants (rectanges) you have selected For the simplifcation on your
homework sheet.)
Be careFul, this is a tricky one, make sure you choose essential prime
implicants frst!
F
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 Spring '07
 Cyganski
 Logic, Boolean Algebra, Karnaugh map, Canonical form

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