محول IEEE 754 float

Computers store fractional numbers in binary under the IEEE 754 standard — a sign, an exponent, and a mantissa, packed into a fixed number of bits. This tool shows that representation for any decimal number and parses it back into a number.

How to use it

• Number → bits: enter a decimal number to get its breakdown into sign, exponent, and mantissa for single (32-bit) or double (64-bit) precision.
• Bits → number: paste a bit representation to get the decimal value back.
• Special values (infinity, NaN, signed zero) are recognized and explained separately.

Common uses

• Understanding why 0.1 + 0.2 doesn't exactly equal 0.3 in most programming languages — a concrete demonstration of rounding error.
• Studying float's internal representation to understand precision limits in financial or scientific calculations.
• Parsing a binary dump or network packet where numbers are transmitted in IEEE 754 format.

Things to keep in mind

Most decimal fractions (0.1, for example) have no exact binary representation — that's the root cause of the typical rounding errors seen in calculation results.

Comparing floating-point numbers for exact equality (===) is unreliable — check instead whether the difference is smaller than a small threshold (epsilon).