Question

In order to store floating numbers in computer using the normalized represetation and 32 - bit single precision, the number of bits used for exponent and fraction are _______ , ___________ respectively.
1. 11, 21
2. 16, 15
3. 16, 16
4. 8, 23

Answer 1

Correct Answer - Option 4 : 8, 23

The correct answer is 8,23.

• According to IEEE 754 Standards, IEEE 754 has 3 basic components
• The Sign of Mantissa –
  • This is as simple as the name. 0 represents a positive number while 1 represents a negative number.
• The Biased exponent –
  • The exponent field needs to represent both positive and negative exponents. A bias is added to the actual exponent in order to get the stored exponent.
• The Normalised Mantissa –
  • The mantissa is part of a number in scientific notation or a floating-point number, consisting of its significant digits. Here we have only 2 digits, i.e. O and 1. So a normalized mantissa is one with only one 1 to the left of the decimal.
• For a single-precision IEEE 754 floating-point Standard
  • The sign is of 1 bit.
  • Exponent is of 8 bits
  • The mantissa is of 23 bits.
  • That total combines into 32-bits.