HW1_solution - ECE 2504 Introduction to Computer...

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1 ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 1 Due date: 9/1/09, 11:59 pm Show all work 1. (3 pts) Convert the following binary numbers to decimal: 110011; 10100011; 1100110010. a. 110011 = 1×2 5 + 1×2 4 + 0×2 3 + 0×2 2 + 1×2 1 + 1×2 0 = 32 + 16 + 0 + 0 + 2 + 1 = 51 b. 10100011 = 1×2 7 + 0×2 6 + 1×2 5 + 0×2 4 + 0×2 3 + 0×2 2 + 1×2 1 + 1×2 0 = 128 + 0 + 32 + 0 + 0 + 0 + 2 + 1 = 163 c. 1100110010 = 1×2 9 + 1×2 8 + 0×2 7 + 0×2 6 + 1×2 5 + 1×2 4 + 0×2 3 + 0×2 2 + 1×2 1 + 0×2 0 = 512 + 256 + 0 + 0 + 32 + 16 + 0 + 0 + 2 + 0 = 818 2. (3 pts) Convert the following numbers with the indicated bases to decimal: (20211) 4 ; (13402) 5 ; (13402) 6 . a. (20211) 4 = 2×4 4 + 0×4 3 + 2×4 2 + 1×4 1 + 1×4 0 = 512 + 0 + 32 + 4 + 1 = 549 c. (13402) 6 = 1×6 4 + 3×6 3 + 4×6 2 + 0×6 1 + 2×6 0 = 1296 + 648 + 144 + 0 + 2 = 2090 b. (13402) 5 = 1×5 4 + 3×5 3 + 4×5 2 + 0×5 1 + 2×5 0 = 625 + 375 + 100 + 0 + 2 = 1102
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2 3. (3 pts) Convert the following decimal numbers to binary: 517; 2012; 34463. a. 517 0 1 001 2 0 002 2 0 004 2 0 008 2 0 016 2 0 032 2 0 064 2 1 129 2 0 258 2 r1 517 2 1000000101 Check: = 1×2 9 + 0×2 8 + 0×2 7 + 0×2 6 + 0×2 5 + 0×2 4 + 0×2 3 + 1×2 2 + 0×2 1 + 1×2 0 = 512 + 0 + 0 + 0 + 0 + 0 + 0 + 4 + 0 + 1 = 517 b. 2012
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HW1_solution - ECE 2504 Introduction to Computer...

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