HW5_solution - SOLUTION ECE 2504 Introduction to Computer...

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SOLUTION 1 ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 5 Due date: 28 Sep 09, 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' + abc' + a'b'c' bc a 00 01 11 10 bc a 00 01 11 10 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 f = b'c' + ac' f' = c + a'b f = c ' ( a + b ' ) b. g(a,b,c,d) = abc'd + ab'c'd +abc'd' + ab'cd + abcd' cd ab 00 01 11 10 cd ab 00 01 11 10 00 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 11 1 1 0 1 11 1 1 0 1 10 0 1 1 0 10 0 1 1 0 g = abc' + ab'd + abd' g' = a' + b'd' + bcd O R g = a ( b + d ) ( b ' + c ' + d ' ) g = ac'd + ab'd + abd' c. h(w,x,y,z) = (w'+x+y+z) (w+x+y'+z') (w'+x+y'+z) (w'+x'+y+z) (w'+x+y'+z') (w+x+y+z) yz wx 00 01 11 10 yz wx 00 01 11 10 00 0 1 0 1 00 0 1 0 1 01 1 1 1 1 01 1 1 1 1 11 0 1 1 1 11 0 1 1 1 10 0 1 0 0 10 0 1 0 0 h = y'z + w'x + xy + w'yz' h'= x'y'z' + wy'z' + x'yz + wx'y h = (x+y+z)(w'+y+z)(x+y'+z')(w'+x+y') O R h'= x'y'z' + wy'z' + x'yz + wx'z' h = (x+y+z)(w'+y+z)(x+y'+z')(w'+x+z)
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SOLUTION 2 d. j(w,x,y,z) = wx'z + wxy' + wx'y'z' + w'xy'z' + wx'y + w'x'yz yz wx 00 01 11 10 yz wx 00 01 11 10 00 0 0 1 0 00 0 0 1 0 01 1 0 0 0 01 1 0 0 0 11 1 1 0 0 11 1 1 0 0 10 1 1 1 1 10 1 1 1 1 j = wx' + wy' + xy'z' + x'yz
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HW5_solution - SOLUTION ECE 2504 Introduction to Computer...

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