HW4_solution - ECE 2504 Introduction to Computer...

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ECE 2504 Introduction to Computer Engineering, Fall 2007 Homework 4 Due date: 21 Sep 07, 1:25pm Show all work. 1. (8 pts) Using the Boolean identities, simplify the following Boolean expressions as much as possible. Show all steps. a. x’y’z’+x’yz+xyz x’y’z’+(x’+x)yz x’y’z’+yz b. ((tv’)’(u+w)’)’•(u+w+(t’w’)’)•((tv’)’+(u+w)’) (tv'+u+w)•(u+w+(t’w’)’)•((tv)’+(u+w)’) (u+w+tv’(t’w’)’)•((tv)’+(u+w)’) (u+w+tv’(t+w)) •((t’+v’)+(u’w’)) (u+w+tv’+tvw)(t’+v’+u’w’) (u+tv’+w(1+tv)) (t’+v’+u’w’) (u+w+tv’)(t’+v’+u’w’) c. xy’z’+y’z’+y’z+xy’ y’z’(x+1)+y’x+y’z) y’z’+y’x+y’z y’(z’+z)+y’x y’+y’x y’(1+x) y’ d. (n+p’)n’q’ + (n+p’)(m’pq(m+p)+m’pq(m’p’)) (n+p’)n’q’+(n+p’) (m’pq (m+p)+ m’pq (m+p)’) (n+p’)n’q’+(n+p’) m’pq ((m+p)+ (m+p)’) (n+p’)(n’q’+m’pq) n'q’(n+p’)+m’pq(n+p’) nn’q’+n’p’q’+m’npq+m’pp’q n’p’q’+m’npq 2. (6 pts) Complete problem 1-6 from the text using the following Boolean expression. F = x’yz’ + y’z’ + x’y’z a. F’ =(x’yz’ + y’z’ + x’y’z)’ =(x’yz’)’(y’z’)’(x’y’z)’ F’=(x+y’+z)(y+z)(x+y+z’) =(x+y’+z)(y(x+y+z’) +z(x+y+z’)) =(x+y’+z)(xy+yy+yz’+xz+yz+zz’) =(x+y’)(xy+y+yz’+xz+yz)+z(xy+y+yz’+xz+yz) =x(xy+y+yz’+xz+yz) +y’(xy+y+yz’+xz+yz)+xyz+yz+yzz’+xzz+yzz
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=xxy+xy+xyz’+xxz+xyz+xyy’+yy’+yy’z’+xy’z+yy’z+xyz+yz+yzz’+xzz+yzz =xy+xyz’+xz+xyz+xy’z+yz =xy(1+z’+z)+z(x+xy’+y) =xy+z(x(1+y’)+y) =xy+xz+yz b. FF’= (x’yz’ + y’z’ + x’y’z)(x+y’+z) (y+z) (x+y+z’) = (x’yyz’ + yy’z’ + x’yy’z + x’yzz’ + y’zz’ + x’y’zz) [(x+y’) (x+y+z’) +(xz+yz+zz’)] = (x’yz’ + 0 + 0 + 0 + 0 + x’y’z)(xx+xy+xz’+x y’+y y’+ y’z’+xz+yz+zz’) = (x’yz’+x’y’z)(x+xy+xz’+xy’+0+ y’z’+xz+yz+0) = (x’yz’+x’y’z)(x(1+y+z’+y’+z)+ y’z’ +yz) = (x’yz’+x’y’z)(x+ y’z’ +yz)
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HW4_solution - ECE 2504 Introduction to Computer...

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