Examples
Here are some examples of single-precision IEEE 754 representations:
| Type | Sign | Actual Exponent | Exp (biased) | Exponent field | Significand (fraction field) | Value |
|---|---|---|---|---|---|---|
| Zero | 0 | −127 | 0 | 0000 0000 | 000 0000 0000 0000 0000 0000 | 0.0 |
| Negative zero | 1 | −127 | 0 | 0000 0000 | 000 0000 0000 0000 0000 0000 | −0.0 |
| One | 0 | 0 | 127 | 0111 1111 | 000 0000 0000 0000 0000 0000 | 1.0 |
| Minus One | 1 | 0 | 127 | 0111 1111 | 000 0000 0000 0000 0000 0000 | −1.0 |
| Smallest denormalized number | * | −127 | 0 | 0000 0000 | 000 0000 0000 0000 0000 0001 | ±2−23 × 2−126 = ±2−149 ≈ ±1.4×10−45 |
| "Middle" denormalized number | * | −127 | 0 | 0000 0000 | 100 0000 0000 0000 0000 0000 | ±2−1 × 2−126 = ±2−127 ≈ ±5.88×10−39 |
| Largest denormalized number | * | −127 | 0 | 0000 0000 | 111 1111 1111 1111 1111 1111 | ±(1−2−23) × 2−126 ≈ ±1.18×10−38 |
| Smallest normalized number | * | −126 | 1 | 0000 0001 | 000 0000 0000 0000 0000 0000 | ±2−126 ≈ ±1.18×10−38 |
| Largest normalized number | * | 127 | 254 | 1111 1110 | 111 1111 1111 1111 1111 1111 | ±(2−2−23) × 2127 ≈ ±3.4×1038 |
| Positive infinity | 0 | 128 | 255 | 1111 1111 | 000 0000 0000 0000 0000 0000 | +∞ |
| Negative infinity | 1 | 128 | 255 | 1111 1111 | 000 0000 0000 0000 0000 0000 | −∞ |
| Not a number | * | 128 | 255 | 1111 1111 | non zero | NaN |
| * Sign bit can be either 0 or 1 . | ||||||
Read more about this topic: IEEE 754-1985
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