Robotics/Hardware

32bit Single Precision, the range of value

아슈람 2009. 6. 14. 11:33
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Range Name

Sign (s)
1 [31]

Exponent (e)
8 [30-23]

Mantissa (m)
23 [22-0]

Hexadecimal Range

Range

Decimal Range §

Quiet
-NaN

1

11..11

11..11
:
10..01

FFFFFFFF
:
FFC00001

Indeterminate

1

11..11

10..00

FFC00000

Signaling
-NaN

1

11..11

01..11
:
00..01

FFBFFFFF
:
FF800001

-Infinity
(Negative Overflow)

1

11..11

00..00

FF800000

< -(2-2-23) × 2127

≤ -3.4028235677973365E+38

Negative Normalized
-1.m × 2(e-127)

1

11..10
:
00..01

11..11
:
00..00

FF7FFFFF
:
80800000

-(2-2-23) × 2127
:
-2-126

-3.4028234663852886E+38
:
-1.1754943508222875E-38

Negative Denormalized
-0.m × 2(-126)

1

00..00

11..11
:
00..01

807FFFFF
:
80000001

-(1-2-23) × 2-126
:
-2-149
(-(1+2-52) × 2-150) *

-1.1754942106924411E-38
:
-1.4012984643248170E-45
(-7.0064923216240862E-46) *

Negative Underflow

1

00..00

00..00

80000000

-2-150
:
< -0

-7.0064923216240861E-46
:
< -0

-0

1

00..00

00..00

80000000

-0

-0

+0

0

00..00

00..00

00000000

0

0

Positive Underflow

0

00..00

00..00

00000000

> 0
:
2-150

> 0
:
7.0064923216240861E-46

Positive Denormalized
0.m × 2(-126)

0

00..00

00..01
:
11..11

00000001
:
007FFFFF

((1+2-52) × 2-150) *
2-149
:
(1-2-23) × 2-126

(7.0064923216240862E-46) *
1.4012984643248170E-45
:
1.1754942106924411E-38

Positive Normalized
1.m × 2(e-127)

0

00..01
:
11..10

00..00
:
11..11

00800000
:
7F7FFFFF

2-126
:
(2-2-23) × 2127

1.1754943508222875E-38
:
3.4028234663852886E+38

+Infinity
(Positive Overflow)

0

11..11

00..00

7F800000

> (2-2-23) × 2127

≥ 3.4028235677973365E+38

Signaling
+NaN

0

11..11

00..01
:
01..11

7F800001
:
7FBFFFFF

Quiet
+NaN

0

11..11

10..00
:
11..11

7FC00000
:
7FFFFFFF

§ Your least significant digits may differ.

 

※ Reference website: http://babbage.cs.qc.edu/IEEE-754/References.xhtml

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