HW1_solution - ECE 2504 Introduction to Computer...

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1 ECE 2504 Introduction to Computer Engineering, Fall 2007 Homework 1 1. Convert the following binary numbers to decimal: 100110; 11010111; 1011101100. Show your work. a. 100110 = 1×2 5 + 0×2 4 + 0×2 3 + 1×2 2 + 1×2 1 + 0×2 0 = 32 + 0 + 0 + 4 + 2 + 0 = 38 b. 11010111 = 1×2 7 + 1×2 6 + 0×2 5 + 1×2 4 + 0×2 3 + 1×2 2 + 1×2 1 + 1×2 0 = 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 215 c. 1011101100 = 1×2 9 + 0×2 8 + 1×2 7 + 1×2 6 + 1×2 5 + 0×2 4 + 1×2 3 + 1×2 2 + 0×2 1 + 0×2 0 = 512 + 0 + 128 + 64 + 32 + 0 + 8 + 4 + 0 + 0 = 748 2. Convert the following numbers with the indicated bases to decimal: (22112) 3 ; (34201) 5 ; (205) 7 ; (1872) 9 . a. (22112) 3 = 2×3 4 + 2×3 3 + 1×3 2 + 1×3 1 + 2×3 0 = 162 + 54 + 9 + 3 + 2 = 230 c. (205) 7 = 2×7 2 + 0×7 1 + 5×7 0 = 98 + 0 + 5 = 103 b. (34201) 5 = 3×5 4 + 4×5 3 + 2×5 2 + 0×5 1 + 1×5 0 = 1875 + 500 + 50 + 0 + 1 = 2426 d. (1872) 9 = 1×9 3 + 8×9 2 + 7×9 1 + 2×9 0 = 729 + 648 + 63 + 2 = 1442
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2 3. Convert the following decimal numbers to binary: 549; 2010; 34,725. a. 549 1 001 2 0 002 2 0 004 2 0 008 2 1 017 2 0 034 2 0 068 2 1 137 2 0 274 2 1 549 2 1000101101 Check: = 1×2 9 + 0×2 8 + 0×2 7 + 0×2 6 + 1×2 5 + 0×2 4 + 0×2 3 + 1×2 2 + 0×2 1 + 1×2 0 = 512 + 0 + 0 + 0 + 32 + 0 + 0 + 4 + 0 + 1 = 549 b. 2010 1 0001 2 1 0003 2 1 0007 2 1 0015 2 1 0031 2 0 0062 2 1 0125 2 1 0251 2 0 0502 2 1 1005 2 0 2010
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HW1_solution - ECE 2504 Introduction to Computer...

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