5.21 Simplify the following expression first by using a nap and then by using Boolean aleebra. Use the nmap as a guide to determine which theorenis to apply to which terms for the algebraic simplification. F = a'b'c' + a'c'd + bed + abc + ab' 5.22 Find all prime implicants and all minimum sum-of-products expressions for each of the following functions (a) (A,B,C.D) = E m(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10) (b) f(A,B,C,D) = L m(3, 11, 12, 13, 14) + E d(5,6,7,8,9. 10) (c) fA,B.C,D) = £ m(1,2, 4, 13, 14) + d(5,6,7,8,9, 10) (d) (A,B.CD) = £ m(4, 15) + 2 d(5,6, 7,8,9, 10) (e) f(A,B,C,D) = m(3,4, 11, 15) +£ d(5,6, 7,8,9, 10) () F(A,B,C,D) = I m(4) + E d(5,6,7,8,9, 10, 11, 12, 13, 14) %3D %3D %3D %3D %3! 72 0 1O)
5.21 Simplify the following expression first by using a nap and then by using Boolean aleebra. Use the nmap as a guide to determine which theorenis to apply to which terms for the algebraic simplification. F = a'b'c' + a'c'd + bed + abc + ab' 5.22 Find all prime implicants and all minimum sum-of-products expressions for each of the following functions (a) (A,B,C.D) = E m(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10) (b) f(A,B,C,D) = L m(3, 11, 12, 13, 14) + E d(5,6,7,8,9. 10) (c) fA,B.C,D) = £ m(1,2, 4, 13, 14) + d(5,6,7,8,9, 10) (d) (A,B.CD) = £ m(4, 15) + 2 d(5,6, 7,8,9, 10) (e) f(A,B,C,D) = m(3,4, 11, 15) +£ d(5,6, 7,8,9, 10) () F(A,B,C,D) = I m(4) + E d(5,6,7,8,9, 10, 11, 12, 13, 14) %3D %3D %3D %3D %3! 72 0 1O)
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Transcribed Image Text:Karnaugh Maps 155
5.21 Simplify the following expression first by using a niap and then by using Boolean
alecbra. Use the nap as a guide to determine which theorenis to apply to which
terms for the algebraic simplification.
F = a'b'c' + a'c'd + bcd + abc + ab'
5.22 Find all prime implicants and all mininum sum-of-products expressions for each of
the following functions.
(a) (A,B.C.D) = E m(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10)
(b) f(A,B,C,D) = L m(3, 11, 12, 13, 14) + E d(5,6,7,8,9. 10)
(c) f(A,B.C,D) = £ m(1, 2, 4, 13, 14) + £ d(5, 6, 7,8,9, 10)
(d) (A,B,C.D) = £ m(4, 15) + d(5,6, 7, 8,9, 10)
(e) f(A,B,C,D) = L m(3,4, 11, 15) + £ d(5,6,7,8,9, 10)
() f(A,B,C,D) = I m(4) +E d(5,6,7,8, 9, 10, 11, 12, 13, 14)
(g) fA,B,CD) = £ m(4, 15) + £ d(0, 1, 2,5, 6, 7, 8,9, 10)
5.23 For each function in Problem 5.22, find all minimum product-of-sums expressions.
5.24 Find the minimum sum-of-products expression for
(a) E m(0,2, 3,5,6, 7, 11, 12, 13)
( 6) Σm(2,4,8) +Σ d(0,3, 7)
( c ) Σm(1,5, 6,7, 13 ) + Σ d44,8
(d) f(w, x, y, z) = £ m(0, 3,5, 7, 8,9, 10, 12, 13) + E d(1,6, 11, 14).
(е) П М(0, 1,2,5, 7,9, 11) - П D(4,10, 13)
5.25 Work Problem 5.24 for the following:
(a) f(a, b, c, d) = E m(1,3,4,5,7,9,13, 15)
(b) f(a, b, c, d) = II M(0,3,5, 8, 11)
(c) f(a, b, c, d) = 2 m(0,2, 6, 9, 13, 14) + E d(3,8, 10)
(d) f(a, b, c, d) = II M(0,2,6, 7,9, 12, 13) • II D(1,3,5)
5.26 Find the minimum product of sums for the following. Underline the essential prime
implicants in your answer.
(a) II M(0,2, 4,5, 6, 9,14) • II D(10, 11)
( b) Σm(1 ,3 , 8,9, 15)+ Σd(6,7, 12 )
5.27 Find a minimum sum-of-products and a minimum product-of-sums expression for
each function:
(a) f(A, B, C, D) = II M(0,2, 10, 11, 12, 14, 15) • II D(5,7)
(b) f(w, x, y. z) = E m(0,3, 5,7,8, 9, 10, 12, 13) + 2 d(1,6, 11, 14)
5.28 A logic circuit realizes the function F(a, b, c, d) = a'b' + a'cd + ac'd + ab'd'. Assuming
that a = c never occurs when b = d = 1, find a simplified expression for F.
5.29 Given F= AB'D' + A'B + A'C + CD.
(a) Use a Karnaugh map to find the maxterm expression for F (express your
answer in both decimal and algebric notation).
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