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 × 22
The decimal value corresponding to the above representation (rounded to 2 decimal places) is -7.75