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