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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 : 11110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ______

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Concept:

In IEEE- 754 single-precision format, a floating-point number is represented in 32 bits.

Sign bit (MSB)

Biased Exponent (E’) 

(8 bits)

 Mantissa (M’)

(23 bits)

 

Sign bit value 0 means a positive number, and 1 means a negative number.

The floating-point number can be obtained by formula: (-1)s × 1.M × 2E – 127

Explanation: 

Sign bit

Biased Exponent (E’)

 Mantissa (M’) 

1 10000001  11110000000000000000000

 

Exponent = 10000001 = 129

decimal value = (-1)1 × 1.1111...0 × 2129 – 127 =  (-1)1 ×1.1111 × 2

The decimal value corresponding to the above representation (rounded to 2 decimal places) is -7.75

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