EE 271
– Introduction to Digital Circuits and Systems
HW #3 
Due 1 Feb 2012
1.) For the following circuits, put them into minimized Product of Sums and Sum of Products forms by using a K
map.
Note: to get to Product of Sums, use the Kmap to get the Sum of Products of the function’s inverse, and then
use DeMorgan’s Law.
a.)
D
C
B
A
D
C
B
A
F
Remember,
XOR
.
Also, to evaluate complex
equations you can use a truth table, and evaluate subfunctions first.
b.)
D
C
B
A
D
C
B
A
B
A
D
C
D
C
B
A
2.) A 4input majority gate is, a function that is TRUE when most of its inputs are TRUE, and FALSE when most of
its inputs are FALSE.
Ambiguous situations should be treated as “Don’t Cares”.
If there is more than one possible
solution to the Kmap, pick one.
a.) Produce the Product of Sums and Sum of Products for the 4input majority gate.
b.) Produce the Product of Maxterms and Sum of Minterms form.
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 Winter '09
 Boolean Algebra, Karnaugh map, 4input majority gate, 4input majority, 4input majority gate.

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