IEEE 754-1985
Single precision
Single-precision numbers occupy 32 bits. In single precision: The positive and negative numbers closest to zero (represented by the denormalized value with all 0s in the exponent field and the binary value 1 in the fraction field) are ±2−23 × 2−126 ≈ ±1.40130×10−45 The positive and negative normalized numbers closest to zero (represented with the binary value 1 in the exponent field and 0 in the fraction field) are ±1 × 2−126 ≈ ±1.17549×10−38 The finite positive and finite negative numbers furthest from zero (represented by the value with 254 in the exponent field and all 1s in the fraction field) are ±(2−2−23) × 2¹²⁷ ≈ ±3.40282×10³⁸ Some example range and gap values for given exponents in single precision: As an example, 16,777,217 cannot be encoded as a 32-bit float as it will be rounded to 16,777,216.

IEEE 754-1985

Section Title: Single precision
Table Section Text: Single-precision numbers occupy 32 bits. In single precision: The positive and negative numbers closest to zero (represented by the denormalized value with all 0s in the exponent field and the binary value 1 in the fraction field) are ±2−23 × 2−126 ≈ ±1.40130×10−45 The positive and negative normalized numbers closest to zero (represented with the binary value 1 in the exponent field and 0 in the fraction field) are ±1 × 2−126 ≈ ±1.17549×10−38 The finite positive and finite negative numbers furthest from zero (represented by the value with 254 in the exponent field and all 1s in the fraction field) are ±(2−2−23) × 2¹²⁷ ≈ ±3.40282×10³⁸ Some example range and gap values for given exponents in single precision: As an example, 16,777,217 cannot be encoded as a 32-bit float as it will be rounded to 16,777,216.

Actual Exponent (unbiased)	Exp (biased)	Minimum	Maximum	Gap

−1	126	0.5	≈ 0.999999940395	≈ 5.96046e-8

0	127	1	≈ 1.999999880791	≈ 1.19209e-7

1	128	2	≈ 3.999999761581	≈ 2.38419e-7

2	129	4	≈ 7.999999523163	≈ 4.76837e-7

10	137	1024	≈ 2047.999877930	≈ 1.22070e-4

11	138	2048	≈ 4095.999755859	≈ 2.44141e-4

23	150	8388608	16777215	1

24	151	16777216	33554430	2

127	254	≈ 1.70141e38	≈ 3.40282e38	≈ 2.02824e31

Sentence(s)

In single precision, the bias is 127.

final_sentence: In single precision, the bias is 127.