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Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S: 1 E: 10000001 F: 11100000000000000000000 Here S, E and F denote the sign, exponent and fraction components of the floating point representation. The above representation (rounded to 2 decimal places) is

1. -7.00
2. -7.50
3. -15.00
4. -15.50

Correct answer: -7.50

Solution

E=10000001=129 so exponent=129-127=2, and mantissa 1.111b = 1.875; with sign bit 1 the value is -1.875 x 2^2 = -7.50. The stored -15.50 is wrong.

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