ee101_hw4_fall06_sol

ee101_hw4_fall06_sol - EE 101 Homework 4 Fall '06 Redekopp...

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1 EE 101 Homework 4 Fall ’06 Redekopp Name: ___Solutions_____________________________ Lecture 9:30 / 12:30 / 5:00 Due: Tues. Sept. 26 th in class Score: ________ Show work to get full credit. Remember, use on only one side of the paper and staple them together. Only use a calculator to CHECK your work, not to DO your work. 1.a x’ = x NOR 0 x x’ 0 or inversion can be achieved as x x 1.b According to DeMorgan’s theorem, x·y = () x y + xy x 0 y 0y 1.c x + y = x y + x y 0 x + y
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2 1.d 1.a, 1.b, and 1.c can all be accomplished only using NAND gates. (a) x’ = x NAND 1 x x’ 1 or x x x’ (b) x·y = () x y x y 1 xy (c) x + y = x y -- DeMorgan’s theorem x+y x 1 y 1 y’
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3 2.a F = (A + B’)C’D + C’(A + B’)D’ + D(A + B’) = AC’D + B’C’D + AC’D’ +B’C’D’ + AD + B’D = AC’(D + D’) + B’C’(D + D’) + AD + B’D = AC’ + B’C’ + AD + B’D 2.b G = ()( ) ( ( ) ) wxy w x y w zx y xwz ++ + + + ⋅ + = () ( ) ( ) x y x wz ⋅++ + + ⋅+ + -- DeMorgan’s theorem = ( ) wxy wxy wz xy x wz ++ + + = wxy wxy wxz xxy wwzz wxyz ++++ + = 0 ww x yw x z w zw x y z + + + -- 0 xx = = x x x y z + = (1 ) x z x w x y z + -- 11 x + = = x x y z = ) x z x y -- xy + = = x z + 3.a SOP = A BB CB C Alternately: B’C’ + A’C’ + BC POS = (B+C’)(A’+B’+C) 1 0 1 1 1 1 6 4 5 7 3 1 00 01 11 10 0 1 2 AB C 0 0 0 0 6 4 5 7 3 1 00 01 11 10 0 1 2 AB C
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4 3.b SOP = YZ WY WXZ WXYZ ++ + POS = ( ) () ( ) YZWXYWXYWYZ + 3.c
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ee101_hw4_fall06_sol - EE 101 Homework 4 Fall '06 Redekopp...

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