Name

Half

Single

Double

Bytes

2

4

8

Bits = sign + exponent + significand

16 = 1 + 5 + 10

32 = 1 + 8 + 23

64 = 1 + 11 + 52

Exponent bias, range

15, −14 … 15

127, −126 … 127

1023, −1022 … 1023

Significant decimal digits

≈ 3.311

≈ 7.225 (6 … 9)

≈ 15.955 (15 … 17)

Minimum positive subnormal

2−24 ≈ 5.96 × 10−8

2−149 ≈ 1.4 × 10−45

2−1022-52 ≈ 5 × 10−324

Minimum positive normal

2−14 ≈ 6.10 × 10−5

2−126 ≈ 1.18 × 10−38

2−1022 ≈ 2.2250738585072014 × 10−308

Next value after 1

1 + 2−10 = 1.0009765625

1 + 2−23 ≈ 1.0000001

1 + 2−52 ≈ 1.0000000000000002

Integers represented exactly

0 … 211 = 2048

0 … 224 = 16,777,216

0 … 253 = 9,007,199,254,740,992

Maximum

(2−2−10) × 215 = 65504

(2−2−23) × 2127 ≈ 3.4 × 1038

(1 + (1 − 2−52)) × 21023 ≈ 1.7976931348623157 × 10308

0.0

0000

00000000

00000000 00000000

1.0

3C00

3F800000

3FF00000 00000000

-1.0

BC00

BF800000

BFF00000 00000000

0.5

3800

3F000000

3FE00000 00000000

2.0

4000

40000000

40000000 00000000

Example NaN

FFFF

FFFFFFFF

FFFFFFFF FFFFFFFF

Exponent (binary)

Significand (binary)

Meaning

000…0

000…0

−0 / +0

000…0

Non-zero