What is the difference between single and double precision?

Single precision (binary32) uses 32 bits: 1 sign, 8 exponent, and 23 mantissa, giving about 7 decimal digits of precision. Double precision (binary64) uses 64 bits: 1 sign, 11 exponent, and 52 mantissa, giving about 15 to 16 digits. Double is the default float type in most languages; single is common on GPUs and in memory-constrained code.

Why does 0.1 not convert to an exact value?

0.1 has no finite representation in binary floating point, just as 1/3 has no finite decimal. The closest representable double is 0.1000000000000000055511151231257827021181583404541015625. In Single (32-bit) mode the converter's Stored value shows the rounding directly as 0.10000000149011612. In Double (64-bit) mode it shows 0.1, because the value is printed as the shortest decimal that maps back to the same bits; the mantissa bits, ending in 1010 rather than repeating 1001 forever, are where the rounding shows.

What are the sign, exponent, and mantissa?

The sign bit is 0 for positive and 1 for negative. The exponent field stores a power of two with a bias added (127 for single, 1023 for double), which is why the tool shows both the biased value in the bits and the unbiased power it applies. The mantissa holds the fractional part of the significand, with an implied leading 1 for normal numbers.

Can I convert IEEE 754 bits back to a decimal number?

Yes. Set the input type to Hex or Binary and paste the exact bit pattern: 8 hex digits or 32 bits for single precision, 16 hex digits or 64 bits for double. The tool decodes it and shows the decimal value it represents along with the full field breakdown.

How are infinity, NaN, and zero represented?

When every exponent bit is 1, an all-zero mantissa means infinity and a non-zero mantissa means NaN. When every exponent bit is 0, an all-zero mantissa is zero (positive or negative depending on the sign bit) and a non-zero mantissa is a subnormal number. The converter labels each of these cases for you.

Why does 16777217 come back as 16777216 in single precision?

Because single precision cannot hold every integer above 16,777,216, which is 2 to the power 24. With only 23 mantissa bits, the gap between neighbouring representable values there is 2, so 16777217 rounds to 16777216 and the converter shows that in the Stored value with hex 4B800000. Double precision holds every integer up to 2 to the power 53 exactly, so switch to Double (64-bit) when whole numbers must survive.

Does this IEEE 754 converter support half precision or 80-bit values?

No. It covers the two formats almost every language uses: binary32 (single) and binary64 (double). Half precision (binary16), quadruple precision (binary128) and the 80-bit x87 extended format are not available, and hex or binary input must be exactly 8 or 16 hex digits, or 32 or 64 bits, to match the precision you picked.

Is it safe to use this tool for sensitive numbers?

Yes. The conversion runs entirely in JavaScript in your browser. No network request carries your input, nothing is stored, and the tool works offline once the page has loaded, so any value you enter stays on your device.

What hex format does the converter expect?

Plain hexadecimal digits, with an optional 0x prefix and spaces or underscores for grouping, which are ignored. Single precision expects 8 hex digits and double precision expects 16. For example, 40490FDB is single-precision pi (3.1415927).

Is this IEEE 754 converter free?

Yes, free and with no account. Both precisions, both directions and the sign, exponent and mantissa breakdown are available to everyone; there is no paid tier, because the conversion is done by your browser and costs nothing per use. Nothing you type is sent anywhere, which also matters when the number came out of a debugger.

IEEE 754 Converter

Convert a decimal number to its IEEE 754 floating-point bits, or decode hex and binary back to a value. Single and double precision, with sign, exponent, and mantissa broken out.

Precision:

Input:

Decimal number

What is an IEEE 754 Converter?

An IEEE 754 converter shows how a computer stores a floating-point number. Enter a decimal value like 3.14159 and the tool encodes it into the exact bit pattern defined by the IEEE 754 standard, splitting the result into its three parts: the sign bit, the exponent field, and the mantissa (also called the fraction or significand). It works in both directions, so you can also paste a 32-bit or 64-bit binary string, or its hexadecimal equivalent, and decode it back into the number it represents.

Used as an IEEE 754 floating point converter, it makes the classic 0.1 problem visible. Choose Single (32-bit), keep Decimal, enter 0.1 and click Convert: the hexadecimal is 3DCCCCCD, the biased exponent is 123 (unbiased 2^-4), and the Stored value reads 0.10000000149011612. Switch to Double (64-bit) and the same input gives 3FB999999999999A, yet the Stored value shows 0.1, because a double is printed as the shortest decimal that reads back to the same 64 bits.

Floating-point numbers are not stored the way we write them. A value is kept as a sign, a power of two, and a fractional significand, following the scheme in IEEE 754-2019. That design is why 0.1 plus 0.2 does not equal exactly 0.3, why some decimals round when stored, and why very large and very small magnitudes are possible in the same 32 or 64 bits. Seeing the sign, exponent, and mantissa laid out makes these behaviours concrete instead of mysterious, which helps when you are debugging a numeric bug, writing a serializer, studying computer architecture, or comparing single and double precision.

This tool runs client-side and uses the same ArrayBuffer and DataView primitives the JavaScript engine uses internally, so the bit patterns match what your CPU would produce, down to the rounding. Single precision (binary32) uses 1 sign bit, 8 exponent bits, and 23 mantissa bits; double precision (binary64) uses 1 sign bit, 11 exponent bits, and 52 mantissa bits. The special cases are handled too: positive and negative zero, subnormal numbers, infinity, and NaN are each identified. Nothing you enter is uploaded, and the tool keeps working offline once loaded.

How to use the IEEE 754 Converter?

Pick single or double precision
Choose single (32-bit, binary32) or double (64-bit, binary64). Double is the default for most languages, so pick it unless you are targeting float specifically.
Choose your input type
Select Decimal to encode a number, or Hex or Binary to decode an existing bit pattern back into a value. Special inputs like Infinity, -Infinity, and NaN are accepted in decimal mode.
Enter your value
Type a decimal number such as 3.14159 or 6.022e23, or paste the exact number of hex digits or bits the precision requires. The conversion updates as soon as you convert.
Read the breakdown and copy
See the sign, exponent, and mantissa split out, along with the full bits, hex, biased and unbiased exponent, and the stored value read back from the bits. Each row of the table has its own copy button.

Single and double precision, side by side

A float is three fields packed into a fixed number of bits: one sign bit, an exponent, and the mantissa that holds the digits. How many bits each field gets is the entire difference between a 32-bit and a 64-bit number, and it is what decides where precision runs out.

Bit layout of IEEE 754 binary32 and binary64
Field	Single (32-bit)	Double (64-bit)
Sign	1 bit	1 bit
Exponent	8 bits	11 bits
Mantissa	23 bits	52 bits
Exponent bias	127	1023
Total	4 bytes	8 bytes

Key Features

Single and Double Precision
Convert to binary32 (1 + 8 + 23 bits) or binary64 (1 + 11 + 52 bits), the two formats used by float and double in nearly every language.
Both Directions
Encode a decimal number into bits, or decode a binary or hexadecimal bit pattern back into the value it represents, without switching tools.
Sign, Exponent, Mantissa Split
The result is broken into its three fields, with both the biased exponent stored in the bits and the unbiased power-of-two it applies.
Special Values Detected
Positive and negative zero, subnormal numbers, infinity, and NaN are each identified so you can see exactly which case a bit pattern falls into.

Frequently Asked Questions

Choose single or double precision, keep the input type on Decimal, type your number, and convert. The tool encodes the value into its IEEE 754 bit pattern and shows the sign bit, exponent field, mantissa, full binary, and hexadecimal. All of it runs in your browser.

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Read the full IEEE 754 Converter guide

Command Palette

IEEE 754 Converter

What is an IEEE 754 Converter?

How to use the IEEE 754 Converter?

Pick single or double precision

Choose your input type

Enter your value

Read the breakdown and copy

Single and double precision, side by side

Key Features

Single and Double Precision

Both Directions

Sign, Exponent, Mantissa Split

Special Values Detected

Frequently Asked Questions

Related Tools

ASCII Table

Binary Calculator

Binary Translator

Morse Code Translator

Comments

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