🧮 Floating-Point Calculator
See exactly how a decimal number is stored in memory as an IEEE 754 single or double precision floating-point value.
How Computers Store Decimal Numbers
Computers represent real (non-integer) numbers using the IEEE 754 floating-point standard, which splits a number into three parts: a sign bit, an exponent, and a mantissa (also called the significand). This calculator shows how your entered decimal number breaks down into those parts.
The Format
A 32-bit single-precision float uses 1 sign bit, 8 exponent bits (biased by 127), and 23 mantissa bits. A 64-bit double-precision float uses 1 sign bit, 11 exponent bits (biased by 1023), and 52 mantissa bits. The final value is reconstructed as (-1)sign × 1.mantissa × 2exponent.
This is why some decimal fractions (like 0.1) can’t be represented exactly in binary floating-point, which is a common source of small rounding differences in software. Useful for programming, computer science education, and debugging numeric precision issues.