IEEE 754 Single Decoder

About this calculator

IEEE 754 single-precision is the 32-bit binary format almost every programming language uses for the float type. The bits break down into three fields: 1 sign bit, an 8-bit exponent stored with a bias of 127, and a 23-bit mantissa (fraction) representing the significant digits after an implied leading 1. The final value is (−1)^sign × 1.mantissa × 2^(exponent−127).

This decoder takes 8 hex digits — the raw bit pattern of a float — and splits them back into those three fields, then reconstructs the decimal value. It’s a everyday reference for software engineers and computer science students debugging serialization bugs, inspecting memory dumps, or learning why floating-point numbers round the way they do, as well as for embedded and low-level programmers who need to see exactly how a value is represented in hardware.