sp07-jh-s1 - ECE 2030 - Introduction to Computer...

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ECE 2030 -- Introduction to Computer Engineering EXAM #1 SOLUTION February 2, 2007 Page 1 of 3 Problem 1. (16 points) A. (7 points) (i) 100101101 2 = 2 8 + 2 5 + 2 3 + 2 2 + 2 0 = 256 + 32 + 8 + 4 +1 = 301 10 (ii) 182 10 = 128 + 32 + 16 + 4 +2 = 2 7 + 2 5 + 2 4 + 2 2 + 2 1 = 10110110 2 (iii) 10011101 2 = 010 011 101 2 = 235 8 (iv) 637 8 = 6x8 2 + 3x8 1 + 7x8 0 = 6x64 + 3x8 + 7x1 = 384 + 24 + 7 = 415 10 (v) 6D9 16 = 0110 1101 1001 2 = 11011011001 2 (vi) 703 10 = 2x256 + 11x16 + 15 = 2x16 2 + 11x16 1 + 15x16 0 = 2BF 16 (vii) B5D9 16 = 1011 0101 1101 1001 2 = 001 011 010 111 011 001 2 = 132731 8 B. (9 points) (i) (A + B) (A + C) (B + C) = (A A + A C + B A + B C) (B + C) = A C B + A C C + B A B + B A C + B C B + B C C = A B C + A B + A B C + B C = A B (C + 1 + C) + B C = A B + B C (U) (ii) (A + C + D) (B + C D) = (A + C D) (B + C + D) = A B + A C + A D + C D B + C D C + C D D = A B + A C + A D + C D (B + 1) = A B + A C + A D + C D (Q) (iii) A + C + B + (D + A) = A C + B (D + A) = A C + B (D A) = A C + A B D
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sp07-jh-s1 - ECE 2030 - Introduction to Computer...

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