Your Name__________________________________________________________________________________
Question 2 :Boolean Logic Theory (15 points)
Draw the circuit producing the function
f(A,B,C,D) =
Σ
m(8,9,10,11,12,13,15) and using
ONLY
the building
block
g(x,y,z) = x
f8e5
y +
x z. Two such blocks are sufficient.
(5 points)
a)
Explain
CLEARLY
your approach to solve this problem.
(5 points)
b)
Decompose f
in terms of
g.
(5 points)
c)
Draw the complete minimal circuit.
_________________________________________________________________
ANSWER
a)
We map on a K-map the function
f . If
f is not a Booean constant (0,1) or one of the input variables or
their complement, it must be the output of a building block g. Now we try to express x, y, z
as functions
of
A, B, C, D and determine if these functions are Boolean constants,
input variables or their
complement. If any of them
are not, again,
they must be outputs of a bulding block
g. We iterate this
process until input variables or their complement are found. If g is complete, the process converges. If
not, there is no solution.
This process is illustrated by the following figure: