hw1sol

# hw1sol - CSE140 Spring 2010, Homework #1 Solution 1. a. F...

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CSE140 – Spring 2010, Homework #1 Solution 1. a. F (A,B,C) = A’ B’ C’ + A’ B’ C + A B’ C’ + A B’ C + A B C’ + A B C = A’B’ (C’ + C) + AB’ (C’ + C) + AB (C’ + C) [ Complementarity] = A’B’ + AB’ + AB = A’B’ + AB’ + AB’ +AB [ Idempotency] = B’ (A’ + A) + A (B’ + B) [ Complementarity] = B’ + A b. F(A,B) = (A’+B) ( A+B) = AA’ + A’B+ AB+ BB [Complementarity ] = A’B+AB+BB = B ( A’+A+1) [Complementarity , Idempotency ] = B . 1 [ identity ] = B 2. 3.

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4. a. (F23) 16 --> ( ) 10 3 *16^0=3 2* 16^1=32 F*16^2= 3840 (F23) 16 --> (3875 ) 10 = 3+32+3840 = 3875 b. (1E0) 16 --> ( ) 2 0 * 16^0=0 E * 16^1=224 1 * 16^2=256 =224+256 = 480 10 2|480 2|240 - 0 2|120 – 0 2|60 – 0 (1E0) 16 --> (111100000 ) 2 2|30 – 0 2|15 – 0 2|7 – 1 2|3 – 1 1–1
c. (10011111) 2 --> ( ) 8 1*2^0= 1 1*2^1=2 1*2^2=4 1*2^3=8 1*2^4=16 0*2^5=0 0*2^6=0 1*2^7=128 = 159 10 8|159 8|19 – 7 |2 – 3 (10011111) 2 --> (237 ) 8 d. (104) 10 --> ( ) 2 2|104 2|52 – 0

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## hw1sol - CSE140 Spring 2010, Homework #1 Solution 1. a. F...

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