su09-jh-s1 - ECE 2030 - Introduction to Computer...

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ECE 2030 -- Introduction to Computer Engineering EXAM #1 SOLUTION June 10, 2009 Page 1 of 4 Problem 1. (20 points) A. (8 points total; 2 pts for part vii) (i) 101001011 2 = 2 8 + 2 6 + 2 3 + 2 1 + 2 0 = 256 + 64 + 8 + 2 +1 = 331 10 (ii) 181 10 = 128 + 32 + 16 + 4 +1 = 2 7 + 2 5 + 2 4 + 2 2 + 2 0 = 10110101 2 (iii) 10101110 2 = 010 101 110 2 = 256 8 (iv) 574 8 = 5x8 2 + 7x8 1 + 4x8 0 = 5x64 + 7x8 + 4x1 = 320 + 56 + 4 = 380 10 (v) 6D5 16 = 0110 1101 0101 2 = 11011010101 2 (vi) 603 10 = 2x256 + 5x16 + 11 = 2x16 2 + 5x16 1 + 11x16 0 = 25B 16 (vii) B9C3 16 = 1011 1001 1100 0011 2 = 001 011 100 111 000 011 2 = 134703 8 B. (12 points) (i) (P) Σ m (3, 5, 6) = A B C + A B C + A B C (ii) (S) Π M (0, 1, 2, 5, 6) = Σ m (3, 4, 7) = A B C + A B C + A B C (iii) (U) (A + B) (A + B + C) (B + C) = (A A + A B + A C + B A + B B + B C) (B + C) = (A B + A C + A B + B C) (B + C) = A C B + A B + B C + A B C + A B C = B C (A + 1) + A B (1 + C) + A B C = A B C + A B + B C (iv) (R) (B + C + D) + (A + B D) + A B D = B C D + A B D + A B D
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su09-jh-s1 - ECE 2030 - Introduction to Computer...

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