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HomeworkSolutions1 - ECE 171 Winter 2011 Homework 1...

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Unformatted text preview: ECE 171 Winter 2011 Homework 1 Solutions 1. [5] Use the “subtract the weights” or “repeated radix division” method to convert each of the following decimal integers to binary. a) 13 a) 1101 b) 35 b) 100011 c) 47 c) 101111 d) 74 d) 1001010 e) 165 e) 10100101 2. [5] Convert each of the following binary numbers to its equivalent hexadecimal representation using the “groups of 4” method. a) 10000101 a) 85 b) 10010110 b) 96 c) 10110111 c) B7 d) 11011100 d) DC e) 11111011 e) FB 3. [5] Convert each of the following hexadecimal numbers to its equivalent binary representation using the “groups of 4” method in reverse. a) D a) 1101 b) 1A b) 0001 1010 c) 16 c) 0001 0110 d) 321 d) 0011 0010 0001 e) BEAD e) 1011 1110 1010 1101 4. [10] Convert each of the following binary numbers to its equivalent octal and hexadecimal representations. a) 10000001 a) 8116 = 2018 b) 101010100 b) 15416 = 5248 c) 10001000.111 c) 88.E16 = 210.78 d) 1100001.1 d) 61.816 = 141.48 e) 110111.01 e) 37.416 = 67.28 5. [5] Convert each of the following hexadecimal numbers to its decimal equivalent using the polynomial function method. a) 1516 a) 2110 b) B216 b) 17810 c) 10D16 c) 26910 d) EE16 d) 23810 e) 7C16 e) 12410 6. [5] Fill in the table below 20 21 22 23 24 25 26 27 28 29 210 Decimal 1 2 4 8 16 32 64 128 256 512 1024 Binary 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 Octal 1 2 4 10 20 40 100 200 400 1000 2000 Hexadecimal 1 2 4 8 10 20 40 80 100 200 400 7. [5] Construct a table showing the hexadecimal numbers between 00 and 20 and their corresponding binary equivalents. Hexadecimal 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 Binary 0000 0000 0000 0001 0000 0010 0000 0011 0000 0100 0000 0101 0000 0110 0000 0111 0000 1000 0000 1001 0000 1010 0000 1011 0000 1100 0000 1101 0000 1110 0000 1111 0001 0000 0001 0001 0001 0010 0001 0011 0001 0100 0001 0101 0001 0110 0001 0111 0001 1000 0001 1001 0001 1010 0001 1011 0001 1100 0001 1101 0001 1110 0001 1111 0010 0000 8. [6] Convert the decimal number 0.625 to its binary, octal, and hexadecimal equivalents. 0.62510 = 0.1012 = 0.58 = 0.A16 9. [6] Convert the decimal number 13.9 to its binary, octal, and hexadecimal equivalents. 13.910 = 1101.111002 = 15.714638 = D.E616 Note: The underscored fractional portion of the binary equivalent repeats. Because the original decimal number is given to a single decimal of precision, or one part in 10, we only require the same of the binary number, or one part in about 16 (about 4 bits). Acceptable answers for octal and hexadecimal depend upon the number of binary bits you’re considering and whether you considered the repeating pattern. Thus if you used 1101.1110 for the binary equivalent then you’d obtain 15.78 and D.E16. ...
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