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Problem 28

Convert each of the following excess 32 representations to its equivalent base 10 representation: a. 011111 b. 100110 c. 111000 d. 000101 e. 010101

Problem 30

Convert each of the following two's complement representations to its equivalent base 10 representation: a. 010101 b. 101010 c. 110110 d. 011011 e. 111001

Problem 31

Convert each of the following base 10 representations to its equivalent two's complement representation in which each value is represented in 8 bits: a. 27 b. 3 d. 8 c. 18 c. 21

Problem 32

Perform each of the following additions assuming the bit strings represent values in two's complement notation. Identify each case in which the answer is incorrect because of overflow. a. 00101+01000 b. 11111+00001 c. 01111+00001 d. 10111+11010 c. 11111+11111 f. 00111+01100

Problem 34

Convert each of the following binary representations into its equivalent base ten representation: a. 11.11 b. 100.0101 c. 0.1101 d. 1.0 c. 10.01

Problem 41

Explain how errors can occur when measurements using the metric system are recorded in floating-point notation. For example, what if 110 cm was recorded in units of meters?

Problem 42

One of the bit patterns 01011 and 11011 represents a value stored in excess 16 notation and the other represents the same value stored in two's complement notation. a. What can be determined about this common value? b. What is the relationship between a pattern representing a value stored in two's complement notation and the pattern representing the same value stored in excess notation when both systems use the same bit pattern length?

Problem 45

If you changed the length of the bit strings being used to represent integers in binary from 4 bits to 6 bits, what change would be made in the value of the largest integer you could represent? What if you were using two's complement notation?

Problem 46

What would be the hexadecimal representation of the largest memory address in a memory consisting of 4MB if each cell had a one-byte capacity?

Problem 47

What would be the encoded version of the message xxy yyx xxy xxy yyx if LZW compression, starting with the dictionary containing x,y, and a space (as described in Section 1.8), were used?

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