🔣IEEE 754 Converter
Convert a decimal number to its IEEE 754 binary32 or binary64 representation.
Free IEEE 754 Converter
This IEEE 754 converter shows exactly how a decimal number is stored in memory as a binary32 (single-precision) or binary64 (double-precision) floating-point value. It breaks the result into its three parts — sign bit, exponent, and mantissa (fraction) — and shows the hexadecimal representation of the raw bits.
Binary32 uses 1 sign bit, 8 exponent bits, and 23 mantissa bits; binary64 uses 1 sign bit, 11 exponent bits, and 52 mantissa bits. Many decimal values — like 0.1 — can't be represented exactly in binary floating-point, which is why floating-point rounding errors happen.
Useful for computer science coursework, debugging floating-point precision issues, and low-level programming. Free, runs entirely in your browser.
About the IEEE 754 Converter
Features
Binary32 and binary64
Single and double precision, side by side.
Color-coded bits
Sign, exponent, and mantissa clearly separated.
Hex output
The raw bit pattern in hexadecimal.
Instant, private
Runs entirely in your browser. No data is sent anywhere.
Frequently Asked Questions
What is IEEE 754?
IEEE 754 is the standard format nearly all computers use to represent floating-point (decimal) numbers in binary, defining how the sign, exponent, and fraction bits are laid out.
What's the difference between binary32 and binary64?
Binary32 (single precision) uses 32 bits total (1 sign, 8 exponent, 23 mantissa); binary64 (double precision) uses 64 bits (1 sign, 11 exponent, 52 mantissa), giving roughly double the decimal precision.
What does the sign bit do?
0 means the number is positive; 1 means it's negative — it's the leftmost bit in the representation.
What is the exponent field?
It stores the power of 2 the number is scaled by, offset by a fixed 'bias' (127 for binary32, 1023 for binary64) so the stored exponent is always a non-negative integer.
What is the mantissa (fraction)?
The mantissa stores the significant digits of the number after an implicit leading 1, representing the number in the form 1.fraction × 2^exponent.
Why can't 0.1 be represented exactly?
0.1 in binary is an infinitely repeating fraction (like 1/3 in decimal), so it must be rounded to fit in a finite number of mantissa bits — this rounding is the source of many classic floating-point precision bugs.
What does the 'stored value (rounded)' show?
It's the actual decimal value the bits represent after rounding to the chosen precision — for values that convert exactly, this matches your input; for others, it shows the nearest representable value.
What is the hex representation used for?
It's a compact way to write the raw 32 or 64 bits, commonly used in debuggers, memory dumps, and low-level programming when working with floating-point values.
Does JavaScript itself use binary64?
Yes — every JavaScript number is a binary64 (IEEE 754 double) value internally, even integers, which is why this converter can compute both formats precisely.
Is this calculator free to use?
Yes, completely free with no sign-up, and it runs entirely in your browser.