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IEEE 754 Converter

Convert decimal numbers to IEEE 754 floating point representation.

0sign
10000000exponent (8 bits)
10010010000111111011011mantissa (23 bits)
Decimal
3.141593
Hex
0x40490FDB
Sign
0 (positive)
Exponent
128 (biased), 1 (actual)

Visualize floating point representation

Convert any decimal number to its IEEE 754 binary representation, or decode a hex value back to decimal. Color-coded bit fields show sign, exponent, and mantissa clearly.

Frequently asked questions

What is IEEE 754?
IEEE 754 is the international standard for floating-point arithmetic. It defines how decimal numbers are stored in binary using a sign bit, exponent bits, and a mantissa (fraction) field.
Why do floating point numbers have rounding errors?
Most decimal fractions cannot be represented exactly in binary. For example, 0.1 in binary is a repeating fraction like 0.0001100110011… truncated at the mantissa length, causing small rounding errors.
What is the difference between float and double?
A 32-bit float has 1 sign bit, 8 exponent bits, and 23 mantissa bits (~7 decimal digits precision). A 64-bit double has 1 sign bit, 11 exponent bits, and 52 mantissa bits (~15 decimal digits precision).

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