IEEE 754 Notation

3. Creating the Bitstring

You're almost done when the number is in this form:

(-1)sign bit  *  (1+fraction)  *  2exponent - bias

This was a clever move. Instead of one messy value, you now have three important pieces of information that can identify the number.

When you have calculated these binary values, you can put them into a 32- or 64-bit field. The digits are arranged like this:

Single precision (32-bit) form: (Bias = 127)
(1)sign (8) exponent (23) fraction

Double precision (64-bit) form: (Bias = 1023)
(1)sign (11) exponent (52) fraction

The numbers in parentheses show how many bits are required in each field.

Example: Float to IEEE 754 ->