hw4solns - CMPS 10 Homework Assignment 4 Solutions Problems...

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CMPS 10 - Homework Assignment 4 – Solutions Problems: Chapter 4 (p.184): 1abc, 3abcd, 4ab, 5abc, 6, 7 1.) Given our discussion of positional numbering systems in Section 4.2.1, see whether you can determine the decimal value of the following numbers. a.) 133 (base 4) b.) 367 (base 8, also called octal ). c.) 1BA (base 16, also called hexadecimal. B is the digit that represents 11, A is the digit that represents 10). Solution: a.) (1 x 4 2 ) + (3 x 4 1 ) + (3 x 4 0 ) = 16 + 12 + 3 = 31 Thus, 133 (base 4) = 31 (base 10) b.) (3 x 8 2 ) + (6 x 8 1 ) + (7 x 8 0 ) = 192 + 48 + 7 = 247 Thus 367 (base 8) = 247 (base 10) c.) (1 x 16 2 ) + (11 x 16 1 ) + (10 x 16 0 ) = 256 + 176 + 10 = 442 Thus 1BA (base 16) = 442 (base 10) 3.) Determine the decimal value of the following unsigned binary numbers. a.) 1100 c.) 1111111 b.) 110001 d.) 1000000000 Solution: a.) 2 3 + 2 2 = 8 + 4 = 12 Thus 1100 (base 2) = 12 (base 10) b.) 2 5 + 2 4 + 2 0 = 32 + 16 + 1 = 49 Thus 110001 (base 2) = 49 (base 10) c.) 2 6 + 2 5 + 2 4 + 2 3 + 2 2 + 2 1 + 2 0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 Thus 1111111 (base 2) = 127 (base 10) d.) 2 9 = 512 Thus 1000000000 (base 2) = 512 (base 10) 4.) Using 8 bits, what is the unsigned binary representation of each of the following values: a.) 23 b.) 55 c.) 275
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Solution: a.) 23 = 16 + 4 + 2 + 1 23 = 2 4 + 2 2 + 2 1 + 2 0 Thus 23 (base 10) = 10111 (base 2) b.) 55 = 32 + 16 + 4 + 2 + 1 55 = 2
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