IEEE 754 Float Visualizer
Enter any decimal number to see its 32-bit and 64-bit IEEE 754 binary representation, color-coded by section.
How IEEE 754 Floating-Point Works
IEEE 754 is the technical standard for floating-point arithmetic used in virtually all modern CPUs. A floating-point number is stored in three parts: a sign bit (0 = positive, 1 = negative), a biased exponent (the power of 2, stored with an offset to avoid needing a sign), and a mantissa/fraction (the significant digits, with an implicit leading 1 for normalized numbers).
Single precision (float32) uses 32 bits: 1 sign + 8 exponent + 23 mantissa. The exponent bias is 127. Double precision (float64) uses 64 bits: 1 sign + 11 exponent + 52 mantissa, with a bias of 1023. This is why languages like JavaScript use float64 for all numbers.
Many decimal fractions (like 0.1) cannot be represented exactly in binary — they produce an infinite repeating binary fraction. This is why 0.1 + 0.2 !== 0.3 in most programming languages. The stored value is the nearest representable float.