Homework 4

Max marks: 40

Problem 1 Hazard problem: Design a hazard free SOP for f(A, B, C, D) = Pm(0, 1, 4, 5, 6, 7, 9, 11, 14, 15)

Problem 2 Find the simplest realization of the function f(x1, . . . , x4) = Pm(0, 3, 4, 7, 9, 10, 13, 14),

assuming that the logic gates have a maximum fan-in of two.

Problem 3 Find the minimum-cost circuit for the function f(x1, . . . , x4) = Pm(0, 4, 8, 13, 14, 15).

Assume that the input variables are available in uncomplemented form only. (Hint: Use functional

decomposition.)

Problem 4

P

Use functional decomposition to find the best implementation of the function f(x1, . . . , x5) =

m(1, 2, 7, 9, 10, 18, 19, 25, 31) + D(0, 15, 20, 26). How does your implementa- tion compare with

the lowest-cost SOP implementation? Give the costs.

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