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# HW7 - Ryan Zanski ECE 2504 Introduction to Computer...

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Ryan Zanski ECE 2504 Introduction to Computer Engineering, Summer I 2010 Homework 5 Due date: 7 Jun 10, 11:55pm Show all work. Use LogicWorks to draw circuit diagrams. 1. (20 pts) Determine the minimal SOP and POS forms for the following Boolean expressions using Karnaugh maps. a. f(a,b,c) = ab'c + a'bc + a'b'c + abc' b. g(a,b,c,d) = (a+b'+c+d)(a'+b'+c'+d)(a'+b+c+d)(a+b'+c'+d)(a+b+c+d) =(a’bc’d’)’(abcd’)’(ab’c’d’)’(a’bcd’)’(a’b’c’d’)’ = ((a’bc’d’)+(abcd’)+(ab’c’d’)+(a’bcd’)+ (a’b’c’d’))’ c. h(w,x,y,z) = wx'y'z' + w'xy'z + wx'yz' + wxy'z' + wx'y'z + w'xy'z' 1

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d. j(w,x,y,z) = xyz' + w'xz' + wxyz + wx'yz' + w'x'yz' + w'x'y' 2. (15 pts) Determine a minimal SOP and POS expression for the following Boolean functions together with the don’t care conditions d using a four variable map. Note that don’t care conditions can be set to one value for the SOP solution and the other for the POS solution. a. F(w,x,y,z) = (0,1,2,8,10) d(w,x,y,z) = (3,4,7,9) 2
b. G(w,x,y,z) = Π (0,2,7,8,10,13,15) d(w,x,y,z) = (6,9,12) c. E(w,x,y,z) = (1,2,4,6,7,8,10) d(w,x,y,z) = (0,5,12,14) 3

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3.
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HW7 - Ryan Zanski ECE 2504 Introduction to Computer...

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