Question

In the standard IEEE 754 single precision floating point representation, there is 1 bit for sign, 23 bits for fraction and 8 bits for exponent. What is the precision in terms of the number of decimal digits?  
1. 5
2. 6
3. 7
4. 8

Answer 1

Correct Answer - Option 3 : 7

The correct answer is "option 3".

CONCEPT:

The floating-point representation of a number has three parts:

1. Sign of Mantissa - represent the sign of number {0 - negative, 1 - positive}

2. Exponent - represent both positive & negative exponent.

Bias is added to the actual exponent in order to get stored, exponent.

3.Normalised Mantissa - represent the digits with only one "1" to the left of the decimal.

The value of the Normalised number is (-1)^S x 1.M^E-127

Eg. The floating-point representation for number 85.125:

1.Binary representation of 85.125 → 1010101.001 or 1.010101001 x 26

2.Sign bit → 0 (positive no.)

3.Normalised Mantissa → 010101001

4.Exponent →  127 + 6 = 133  {Bias → 127}

Precision can be by 1.M, so M+1 is used to represent the precise number

23 bits + 1 = 24 bits

According to the formula:

BaseXno. of digits = BaseYno. of digits 

2²⁴ = 10^x

24 = x log₂10

x = 7.22

Hence,  the precision in terms of the number of decimal digits is 7