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.

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