Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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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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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