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hw9_soln - ECE3060 VLSI and Advanced Digital Design Fall...

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ECE3060: VLSI and Advanced Digital Design Fall 2006 Homework #9: due October 26, 4:30pm Solutions Show all your work to get full credit. 1. Consider the following binary function: F ( a; b; c; d ) = ad + a’c’d’ + ab’cd + b’cd + ab’c’ . (a) Represent F using the empty hypercube provided below. (b) Is F an irredundant cover? Explain the reason briefly. No, because F contains an implicant, ab’cd, which can be dropped without changing the function. (c) Is F minimal with respect to single implicant containment? Explain the reason briefly. No, because the implicant ab’cd is contained by another implicant: both ad and b’cd. (d) Is F a prime cover? Explain the reason briefly. No. F is not a prime cover since it contains an implicant ab’cd, which can be expanded into b’cd or into ad. 2. Consider the following binary function F ( a, b, c, d ) = a’b + c ( ab + d’ ) + b c’ . (a) Draw an ROBDD of F under the variable order [ b, a, d, c ]. F = a’b + c(ab + d’) + bc + b’c’ F b = a’ + c(a + d’) + c + 0 = a’ + c(a + d’) + c F b’ = 0 + c(0 + d’) + 0 + c’ = cd’ + c’ = c’ + d’ F ba = 0 + c(1 + d’) + c = c
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