Question

Give 16 bit representation to represent the number -15.25 using the following format:


Sign |------------Exponent -------------------------------------|-------------mantissa ------------------|

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i) Bit 0 should be 0 if the number is positive and 1 if the number is negative.
ii) Exponent should be stored as number in 8th -complement form, (i.e., base=8)

Answer 1

Answer on Question#39687 – Engineering – Other

-15.25 in base-2:

The bias = 2^k-1

Where k = 8 (exponent space)

⇒ Bias = 2^8-1 - 1 = 127

Integral Part 15:

15_10 = 1111_2

Fractional Part 0.25:

0.25 × 2 = 0.50 (remainder = 0)

0.50 × 2 = 1.0 (remainder = 1)

This derives 0.25_10 = 0.10_2

⇒ 15.25_10 = 1111.10_2 = 1.11110 × 2^3

This concludes:

Sign = 1_2 (negative)

Exponent = bias + 3 = 127 + 3 = 130_10 = 202_8 = 100000102

Mantissa = 1111000_2

Hence the decimal after conversion into binary is:

1100 0001 0111 1000 is the required answer.