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Can It Float?

Determine whether a number is exactly representable in IEEE-754 32-bit or 64-bit floating point — and inspect every single bit.

Try: 0.1 0.5 0.3 3.14 0.125 0.1 + 0.2 1 256 -1.5 9007199254740993
32-bit Single Precision
1 sign · 8 exponent · 23 mantissa bits · bias 127
✗ Not Exact
Your Input
0.1
Closest Representable 32-bit Value
0.100000001490116
Hex  ·  Binary (grouped by byte)
0x3DCCCCCD  ·  00111101 11001100 11001100 11001101
Sign (1 bit)
Exponent
Mantissa / Significand
Sign
0
Exponent (8)
01111011
Mantissa (23)
10011001100110011001101
FieldBitsExplanation
Sign 0 0 → positive number (+1 multiplier)
Exponent 01111011 Bits: 01111011₂ = 123 (decimal)
Subtract bias: 123 − 127 = -4
The value is scaled by 2^-4
Mantissa 10011001100110011001101 Fractional part of the significand.
An implicit leading 1 is prepended (for normal numbers).
Full significand: 1.10011001100110011001101₂
Value =
(−1)^0 × 1.10011001…₂ × 2^-4
64-bit Double Precision
1 sign · 11 exponent · 52 mantissa bits · bias 1023
✗ Not Exact
Your Input
0.1
Closest Representable 64-bit Value
0.10000000000000000555111
Hex (64-bit)
0x3FB999999999999A
Sign (1 bit)
Exponent
Mantissa / Significand
Sign
0
Exponent (11)
01111111011
Mantissa (52)
1001100110011001100110011001100110011001100110011010
FieldBitsExplanation
Sign 0 0 → positive number (+1 multiplier)
Exponent 01111111011 Bits: 01111111011₂ = 1019 (decimal)
Subtract bias: 1019 − 1023 = -4
The value is scaled by 2^-4
Mantissa 1001100110011001100110011001100110011001100110011010 52-bit fractional part of the significand.
An implicit leading 1 is prepended (for normal numbers).
Full significand: 1.100110011001…₂
Value =
(−1)^0 × 1.100110011001…₂ × 2^-4
IEEE-754 Standard for Floating-Point Arithmetic  ·  All calculations performed client-side in your browser using JavaScript BigInt for exact decimal conversion
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