Hacker's Delight

15-1. IEEE Format

We will restrict our attention to the single and double formats (32- and 64-bit) described in IEEE 754. The standard also describes “single extended” and “double extended” formats, but they are only loosely described because the details are implementation-dependent (e.g., the exponent width is unspecified in the standard). The single and double formats are shown below.

The sign bit s is encoded as 0 for plus, 1 for minus. The biased exponent e and fraction f are magnitudes with their most significant bits on the left. The floating-point value represented is encoded as shown on the next page.

As an example, consider encoding ...