In IEEE 754 single precision, what is the bias value used for the exponent?

In IEEE 754 single precision, the bias value used for the exponent is 127.

The exponent field in IEEE 754 single precision is an 8-bit unsigned integer, but it is represented with a bias. The bias is added to the actual exponent value to allow for both positive and negative exponents while maintaining a consistent ordering of numbers for arithmetic operations.

The biased exponent is calculated as follows:

  • Actual exponent value + Bias

For single precision, the bias value of 127 is chosen so that:

  • An exponent of 0 (all bits 0 in the exponent field) represents the smallest exponent value, which is -126 after biasing.
  • An exponent of 255 (all bits 1 in the exponent field) represents the largest exponent value, which is +127 after biasing.


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