IEEE 754 is the international standard for floating-point arithmetic. It defines how binary fractions are stored using a sign bit, a biased exponent, and a significand (mantissa). Most CPUs and languages (C, Java, Python, JavaScript) use it.

What is the difference between single and double precision?

Single precision (float) uses 32 bits: 1 sign + 8 exponent + 23 mantissa. Double precision (double) uses 64 bits: 1 sign + 11 exponent + 52 mantissa. Double has roughly twice the decimal digits of precision (~15–17 vs ~6–9).

Why does 0.1 not convert to an exact binary fraction?

0.1 in decimal is a repeating fraction in binary (like 1/3 in decimal). IEEE 754 truncates it to the nearest representable value, introducing a tiny rounding error that accumulates in arithmetic.

What are subnormal numbers?

When the biased exponent field is all zeros, the number is subnormal (denormalized). The implicit leading 1 becomes 0, allowing very small values near zero to be represented at reduced precision.

How are infinity and NaN represented?

When the exponent field is all ones (255 for 32-bit, 2047 for 64-bit): a zero mantissa means ±Infinity; a non-zero mantissa means NaN (Not a Number).

Floating Point Converter

Name: Floating Point Converter
Availability: InStock
Author: Nham Vu

Enter a decimal number and see its IEEE 754 single (32-bit) and double (64-bit) binary floating-point representation with labeled sign, exponent, and mantissa fields.

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Summary

Enter a decimal number and see its IEEE 754 single (32-bit) and double (64-bit) binary floating-point representation with labeled sign, exponent, and mantissa fields.

How it works

Enter any decimal number (integer or floating-point, including negatives).
The tool extracts the sign bit: 0 for positive, 1 for negative.
The value is normalized into the form 1.mantissa × 2^exponent.
The biased exponent is stored (bias = 127 for 32-bit, 1023 for 64-bit).
Mantissa bits are filled by repeatedly multiplying the fractional part by 2.
Results are shown for both 32-bit and 64-bit IEEE 754 formats side by side.

Use cases

Debug floating-point precision issues in low-level code.
Study how IEEE 754 encodes real numbers for computer science courses.
Verify the bit layout of floats when writing C/C++/Rust bit-manipulation code.
Understand why 0.1 + 0.2 ≠ 0.3 in most programming languages.
Cross-check floating-point results when porting code between platforms.
Learn about subnormal numbers, infinities, and NaN representations.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu

Floating Point Converter

Single Precision (32-bit float)

Double Precision (64-bit double)

Bit Field Legend