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5.21 Simplify the following expression first by using a map and then by using Boolcan algebra. Use the nuap 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'

5.21 Simplify the following expression first by using a map and then by using Boolcan algebra. Use the nuap 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'

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Karnaugh Maps 155 5.21 Simplify the following expression first by using a nap and then by using Boolean algebra. Uise the niap 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) f(A.B,C.D) = I im(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10) (b) f(A,B,C,D) = Em(3,11, 12, 13, 14) + E d(5,6,7,8,9. 10) (c) f(A,B.C.D) = I m(1, 2,4, 13, 14) + £ d(5,6,7,8,9, 10) (d) f(A,B,C.D) = E m(4, 15) +2 d(5.6, 7,8,9, 10) (e) (A,B,C,D) = I m(3,4, 11, 15) + E d(5, 6,7,8,9, 10) () F(A,B,C,D) = Im(4) +E d(5,6, 7,8,9, 10, 11, 12, 13, 14) (g) fA,B,CD) = £ m(4, 15) +E 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) ( ) Σmf2 ,4, 8 ) + Σd(0,3,7) (c) E m(1,5,6,7, 13) + E d(4,8) (d) f(w, x, y, z) = £ m(0,3,5, 7,8,9, 10, 12, 13) + E d(1,6, 11, 14) (e) П мо, 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) = E m(0,2, 6, 9, 13, 14) + £ 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) (6) Σm( 1,3,8,9, 15) + Σ d6,7,12 ) 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) +E d(1,6,11, 14) 5.28 A logic circuit realizes the function F(a, b, , 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). الم مسوحة ضوئيا ب CamScan ner
Transcribed Image Text:Karnaugh Maps 155 5.21 Simplify the following expression first by using a nap and then by using Boolean algebra. Uise the niap 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) f(A.B,C.D) = I im(4, 11, 12, 13, 14) + E d(5,6,7,8,9, 10) (b) f(A,B,C,D) = Em(3,11, 12, 13, 14) + E d(5,6,7,8,9. 10) (c) f(A,B.C.D) = I m(1, 2,4, 13, 14) + £ d(5,6,7,8,9, 10) (d) f(A,B,C.D) = E m(4, 15) +2 d(5.6, 7,8,9, 10) (e) (A,B,C,D) = I m(3,4, 11, 15) + E d(5, 6,7,8,9, 10) () F(A,B,C,D) = Im(4) +E d(5,6, 7,8,9, 10, 11, 12, 13, 14) (g) fA,B,CD) = £ m(4, 15) +E 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) ( ) Σmf2 ,4, 8 ) + Σd(0,3,7) (c) E m(1,5,6,7, 13) + E d(4,8) (d) f(w, x, y, z) = £ m(0,3,5, 7,8,9, 10, 12, 13) + E d(1,6, 11, 14) (e) П мо, 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) = E m(0,2, 6, 9, 13, 14) + £ 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) (6) Σm( 1,3,8,9, 15) + Σ d6,7,12 ) 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) +E d(1,6,11, 14) 5.28 A logic circuit realizes the function F(a, b, , 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). الم مسوحة ضوئيا ب CamScan ner
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