The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: sign exponent mantissa Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: sign exponent mantissa Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard? Correct Answer exponent = 00000001 and mantissa = 00000000000000000000000
Option 2) is correct answer.
Concept:
In IEEE- 754 single precision format, a floating-point number is represented in 32 bits.
|
Sign bit (MSB) |
Biased Exponent (E’) (8 bits) |
Normalized 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:
Smallest normalized positive number
|
Sign bit |
Biased Exponent (E’) |
Normalized Mantissa (M’) |
| 0 | 0000 0001 | 00000000000000000000000 |
Smallest normalized positive = (-1)0 × 1.00...0 × 21 – 127 = 2-126 ≈1.1755 × 10–38
