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ch02_complete

# ch02_complete - F.2 Chapter 2 Solutions 2.1 The answer is...

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F.2 Chapter 2 Solutions 2.1 The answer is 2 n 2.2 For 26 characters, we need at least 5 bits. For 52 characters, we need at least 6 bits. 2.3 (a) For 400 students, we need at least 9 bits. (b) 2 9 = 512 , so 112 more students could enter. 2.4 2 n integers can be represented. The range would be 0 to ( 2 n ) - 1. 2.5 If each number is represented with 5 bits, 7 = 00111 in all three systems -7 = 11000 (1’s complement) = 10111 (signed magnitude) = 11001 (2’s complement) 2.6 100000. 2.7 Refer the following table: 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 -8 1001 -7 1010 -6 1011 -5 1100 -4 1101 -3 1110 -2 1111 -1 2.8 The answers are: (a) 127 in decimal, 01111111 in binary. (b) -128 in decimal, 10000000 in binary. (c) ( 2 n - 1 )-1 (d) -( 2 n - 1 ) 1

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2 2.9 Avogadro’s number (6.02 x 10 23 ) requires 80 bits to be represented in two’s complement binary representation. 2.10 The answers are: (a) -6 (b) 90 (c) -2 (d) 14803 2.11 (a) 01100110 (b) 01000000 (c) 00100001 (d) 10000000 (e) 01111111 2.12 It is a multiple of 4. 2.13 (a) 11111010 (b) 00011001 (c) 11111000 (d) 00000001 2.14 (a) 1100 (b) 1010 (c) 1111 (d) 01011 (e) 10000 2.15 Dividing the number by two. 2.16 (a) 11111111 (binary) or -0 (decimal) (b) 10001110 (binary) or -14(decimal) (c) 00000000 (binary) or 0 (decimal) 2.17 (a) 1100 (binary) or -4 (decimal) (b) 01010100 (binary) or 84 (decimal) (c) 0011 (binary) or 3 (decimal) (d) 11 (binary) or -1 (decimal) 2.18 The answers are: (a) 1100 (binary) or 12 (decimal)
F.2. CHAPTER 2 SOLUTIONS

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