Question

For each word length a) determine the range of integers are can represent with sign magnitude, b) write both the positive and negative binary representation in twos-compliemnt of the number provided.

(a) length: 1 bytes, value: 82

(b) length: 12 bits, value: 1124

Answer 1

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a)  determine the range of integers that can be represented with sign magnitude.

b) write the positive and negative numbers of the value given in binary representation in 2's complement format.

(a) length: 1 bytes, value: 82

1 bit is equal to 8 bits.In signed magnitude representation the first bit is taken as 0 for positive numbers and 1 for negative numbers so we are left with only 7 bits.With 7 bits we can get numbers from -127 to 127.

Representing 82 in 2's complement method = 01010010

82 represented in binary is 01010010.

As a positive number it is same so 01010010.

Representing -82 in 2's complement method = 10101110

82 represented in binary is 01010010.

Invert the bits.We get 10101101.

Add 1.We get 10101110.

(b) length: 12 bits, value: 1124

We are given 12 bits.In signed magnitude representation the first bit is taken as 0 for positive numbers and 1 for negative numbers so we are left with only 11 bits.With 11 bits we can get numbers from -2047 to 2047.

Representing 1124 in 2's complement method = 010001100100

1124 in binary is 010001100100.

As a positive number it is same so 010001100100.

Representing -1124 in 2's complement method = 101110011100

1124 in binary is 010001100100

Invert the bits.We get 101110011011.

Add 1 we get 101110011100.