Hw7sol - 1 a See Figure Below a’d a’c’d’ a’b’cd bcd ab’c b F is not an irredundant cover because a’b’cd is a subset that is not

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Unformatted text preview: 1. a. See Figure Below a’d a’c’d’ a’b’cd bcd ab’c b. F is not an irredundant cover, because a’b’cd is a subset that is not needed c. F is not minimal with respect to single implicant containment because a’b’cd is contained by an implicant d. F is not a prime cover because a’b’cd is not a prime implicant 2. a. Group 0 Group 1 Group 2 Group 3 Group 4 01 04 08 15 000* 0*00 *000 0*01 x x x 0 1 4 8 5 6 A 7 B E F 0000 0001 0100 1000 0101 0110 1010 0111 1011 1110 1111 x x x x x x x x x x x 45 46 8A 57 67 6E AE AB 7F BF EF 0145 0415 4567 4657 6E7F ABEF AEBF 010* 01*0 10*0 01*1 011* *110 1*10 101* *111 111* 1*11 x x x x x x x x x x 0*0* 0*0* 01** 01** *11* 1*1* 1*1* F = b’c’d’ + ab’d’ + a’c’ + a’b + bc + ac b. α = b’c’d’ = *000 β = ab’d’ = 10*0 δ = a’c’ = 0*0* ε = a’b = 01** λ = bc = *11* ω = ac = 1*1* a’b’c’d’ a’b’c’d α 1 0 β 0 0 δ 1 1 ε 0 0 λ 0 0 ω 0 0 a’bc’d’ 0 0 1 1 a’bc’d 0 0 1 1 a’bcd’ 0 0 0 1 a’bcd 0 0 0 1 ab’c’d’ 1 1 0 0 ab’cd’ 0 1 0 0 ab’cd 0 0 0 0 abcd’ 0 0 0 0 abcd 0 0 0 0 c. (α + δ)( δ)( δ + ε)( δ + ε)( ε + λ)( ε + λ)( α + β)( β + ω)(ω)( λ + ω) (λ + ω) = (α + δ)( δ)( δ + ε)( ε + λ)( α + β)( β + ω)(ω)( λ + ω) = ( δ)( ε + λ)( α + β)(ω) = α δ ε ω + β δ ε ω + α δ λ ω + β δ λ ω 3. α 1 0 0 0 0 1 α 1 0 0 0 β 0 0 1 1 δ 0 0 0 1 ε 0 1 0 0 λ 1 1 0 1 ω 1 1 1 0 β 0 0 1 1 1 0 δ 0 0 0 1 0 1 ε 0 1 0 0 1 1 λ 1 1 0 1 0 0 ω 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 Assume α is within cover β 0 1 1 0 1 1 0 0 δ 0 0 1 ε 1 0 0 λ 1 0 1 ω 1 1 0 β 0 1 1 Assume α and β are within cover β 0 1 1 λ 1 λ 1 0 1 ω 1 1 0 λ 1 0 1 ω 1 1 0 ω 1 or or Assume α is within cover and β is not λ 1 0 1 Assume α is within cover, β is not, and λ is within cover ω 1 ω 1 1 0 Assume α is within cover, β is not, λ is not, and ω is within the cover Assume α is within cover, β is not, λ is not, and ω is not within the cover Assume α is not within cover β 0 0 1 1 0 β δ 0 0 1 0 1 1 0 1 β δ 0 0 1 0 1 1 0 1 Assume α is not within cover, β is δ 0 λ 1 ω 1 ε 0 0 0 1 λ 1 0 1 0 ω 1 1 0 0 δ 0 0 0 1 1 ε 0 1 0 0 1 λ 1 1 0 1 0 ω 1 1 1 0 0 λ 1 0 1 0 ω 1 1 0 0 1 Assume α is not within cover, β is, δ is 0 0 Assume α is not within cover, β is, δ is not Assume α is not within cover, β is not δ 0 0 1 1 δ 0 1 1 δ 0 ω 1 λ 0 1 0 ω 1 0 0 λ 1 0 1 0 ω 1 1 0 0 1 1 δ 0 1 Assume α is not within cover, β is not, δ is 0 0 ω 1 0 Assume α is not within cover, β is not, δ is not, ω is Assume α is not within cover, β is not, δ is not, ω is not α in Cover α not in Cover β in Cover β not in Cover β in Cover β not in Cover X = [1 1 0 0 1 0] Y = [2 1 1 2 1 1] λ in Cover λ not in Cover δ in Cover δ not in Cover δ in Cover δ not in Cover X = [1 0 0 0 1 1] Y = [3 2 1 1 1 1] ω in Cover ω not in Cover X = [0 1 1 0 0 1] Y = [1 1 2 2 2 1] X = [0 1 0 0 0 1] Y = [1 1 2 1 2 0] X = [0 0 1 0 0 1] Y = [1 1 1 1 1 1] ω in Cover ω not in Cover X = [1 0 0 0 0 1] Y = [2 1 1 0 1 1] X = [1 0 0 0 0 0] Y = [1 0 0 0 0 1] X = [0 0 0 0 0 1] Y = [1 1 1 0 1 0] X = [0 0 0 0 0 0] Y = [0 0 0 0 0 0] ...
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This note was uploaded on 02/19/2010 for the course ECE 3060 taught by Professor Shimmel during the Spring '07 term at Georgia Institute of Technology.

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