Homework 3
Max marks: 70
Note that to find a “minimum-cost circuit”,
you must find both the SOP and POS forms
and compute the cost of each, and then indicate
which is best.
Problem 1 Derive a minimum-cost circuit
P
that implements the function f(x1, . . . , x4) =
m(4, 7, 8, 11) + d(12, 15)
Problem 2 Derive a minimum-cost circuit
P
that implements the function f(x1, . . . , x4) =
m(4, 6, 9, 10, 15) + d(2, 3, 5, 11, 13)
Problem 3 Derive a minimum-cost circuit that
implements the function
f(x1, . . . , x5) = Xm(2, 5, 6, 7, 8, 12, 13, 15,
18, 21, 24, 26, 28, 31)
+ d(1, 4, 14, 23, 25, 29, 30)
Problem 4 Use Quine-McCluskey method to
find the minimal SOP for
P
f(x, y, z) =
m(2, 3, 4, 5). You can also implement QuineMcCluskey method in your favorite programming
language as algorithm.
Problem 5 Use Quine-McCluskey method to
find the minimal SOP for
P
f(x, y, z, w) =
m(0, 1, 4, 5, 12, 13). You can also implement
Quine-McCluskey method in your favorite programming language as algorithm.
Problem 6 Use Quine-McCluskey method to
find the minimal SOP for
P
f(x, y, z, w) =
m(1, 5, 7, 8, 9, 13, 15) + d(4, 14). You can also
implement Quine-McCluskey method in your favorite programming language as algorithm.
Problem 7 A circuit with two outputs has to
implement the following functions
f(x1, . . . , x4) = Xm(0, 2, 4, 6, 7, 9) + d(10, 11)
(1)
g(x1, . . . , x4) = Xm(2, 4, 9, 10, 15) + d(0, 13, 14)
(2)
Design a minimum-cost SOP circuit and compare its cost with combined cost of two SOP circuits that implement f and g separately. Assume
the input variables in both complemented and uncomplemented forms.
1
