hw4s - ENGRD2300 Introduction to Digital Logic Fall 2008...

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ENGRD2300: Introduction to Digital Logic Fall 2008 Homework 4 Solutions Problem 1. Convert the following decimal numbers into binary, octal and hexadecimal. a) 1017 10 = 1111111001 2 = 1771 8 = 3F9 16 b) 623 10 = 10011011112 = 11578 = 26F16 ____ ____ _ c) 19.35 10 = 10011.01011001 2 = 23.26314 8 = 13.59 16 , where the bar indicates a repeating fraction. d) -255 10 = -111111112 = -3778 = -FF16, using minus sign notation = …111000000012 = …774018 = …FF0116 , in infinite-bit 2’s complement Note that the 2’s complement answer isn’t really well defined as we did not specify the number of bits in the representation, so for this problem it does not make sense to be thinking about 2’s complement. You can truncate the infinite-bit 2’s complement answer above to any number of bits 9. Problem 2. Convert the following binary numbers into decimal, octal and hexadecimal. a) 1101011 2 = 107 10 = 153 8 = 6B 16 b) 10100.1101 2 = 20.8125 10 = 24.64 8 = 14.D 16 c) 11001.101 2 = 25.625 10 = 31.5 8 = 19.A 16 d) 1111111 2 = 127 10 = 177 8 = 7F 16 Problem 3. Convert the following 8-bit, 2’s complement numbers into the equivalent 4-bit, 2’s complement and 12- bit, 2’s complement representations. a) 01101011 2 = 1011 2 = 000001101011 2 The 4-bit conversion fails because significant bits are truncated. b) AB 16 = B 16 = FAB 16 The 4-bit conversion fails because significant bits are truncated. c) 257 8 = 17 8 = 0257 8 The 4-bit conversion fails because significant bits are truncated. d) 11111111 2 = 1111 2 = 111111111111 2 Both conversions succeed. Which conversions fail? I.e., cannot be converted properly? 1
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ENGRD2300: Introduction to Digital Logic Fall 2008 Problem 4.
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