Karnaugh Maps 1555.21 Simplify the following expression first by using a niap and then by using Booleanalecbra. Use the nap as a guide to determine which theorenis to apply to whichterms 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 ofthe 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 primeimplicants 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 foreach 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'. Assumingthat 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 youranswer in both decimal and algebric notation).

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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)

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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