IEEE 754-1985 - Examples

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 .

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