Floating-Point Calculator (IEEE 754)

Your details

Enter any real number. The calculator converts it to 32-bit and 64-bit IEEE 754 floating-point binary and shows where precision is lost.
Choose which format drives the primary output card and the visual breakdown.
Sign bitNormal
0

0 = positive, 1 = negative

Exponent bits01111011
Mantissa bits10011001100110011001101
Hexadecimal3DCCCCCD
Stored value0.1000000015
Precision error1.490116e-9
Biased exponent123
True exponent-4
ClassificationNormal
32-bit hex3DCCCCCD
64-bit hex3FB999999999999A
Error (32-bit)1.490116e-9
Error (64-bit)0 (exact)
Biased exponent123
True exponent-4

0.1 in 32-bit single precision: sign=0, exponent=-4 (biased 123), class = Normal.

  • In 32-bit format the stored value differs from your input by 1.490116e-9. This is floating-point rounding in action.
  • 64-bit double precision stores the value with far greater accuracy (about 15-17 significant decimal digits vs. 7 for 32-bit).
  • Binary fractions can only represent numbers whose denominator is a power of 2. Values like 0.1 and 0.3 repeat infinitely in binary, causing the small rounding errors you see.
  • The hexadecimal encodings are: 32-bit = 0x3DCCCCCD, 64-bit = 0x3FB999999999999A.

Next stepUse 64-bit doubles for general computation and reserve 32-bit floats for GPU shaders or large float arrays where memory matters.

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