IEEE754 standard floating point storage format, ieee754 standard floating point

IEEE754 standard floating point storage format, ieee754 standard floating point

Basic storage format (from high to low): Sign + Exponent + Fraction

Sign: Symbol bit

Exponent: Level Code

Fraction: valid number

32-bit floating point Storage Format

Sign: 1 bit (31st bits)

Exponent: 8 bits (8 bits from 30th to 23)

Fraction: 23 bits (23 bits from 22nd to 0)

The true value of a 32-bit non-0 floating point is (python syntax ):

(-1) **Sign * 2 **(Exponent-127) * (1 + Fraction)

Example:

A = 12.5

1. Solve the symbol bit

If a is greater than 0, the Sign is 0, which is expressed as: 0 in binary format.

2. Solving Order Codes

A Indicates binary: 1100.0

If the decimal point needs to be moved three places to the left, the Exponent is 130 (127 + 3), expressed in binary as: 10000010

3. Solving valid numbers

If a valid number needs to be removed from the maximum implicit 1, the integer part of the valid number is: 100.

To convert decimal places to decimal places, use the following method to convert decimal places to decimal places: * 2. If an integer is obtained, the decimal places are: 1.

If the value is 0, the binary value of a can be expressed as: 01000001010010000000000000000000.

That is, 0100 0001 0100 1000 0000 0000 0000 0000

In hexadecimal notation: 0x41480000

4. Restore the true value

Sign = bin(0) = 0Exponent = bin(10000010) = 130Fraction = bin(0.1001) = 2 ** (-1) + 2 ** (-4) = 0.5625

True Value:

(-1) **0 * 2 **(130-127) * (1 + 0.5625) = 12.5

32-bit floating point binary storage Parsing Code (c ++ ):

Https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/floatTest1.cpp

Running effect:

[root@localhost floatTest1]# ./floatToBin1sizeof(float) : 4sizeof(int) : 4a = 12.500000showFloat : 0x 41 48 00 00UFP : 0,82,480000b : 0x41480000showIEEE754 a = 12.500000showIEEE754 varTmp = 0x00c00000showIEEE754 c = 0x00400000showIEEE754 i = 19 , a1 = 1.000000 , showIEEE754 c = 00480000 , showIEEE754 b = 0x41000000showIEEE754 i = 18 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 17 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 16 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 15 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 14 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 13 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 12 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 11 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 10 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 9 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 8 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 7 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 6 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 5 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 4 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 3 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 2 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 i = 1 , a1 = 0.000000 , showIEEE754 b = 0x41000000showIEEE754 : 0x41480000[root@localhost floatTest1]#

Analysis of 64-bit floating point Storage Format

Sign: 1 bit (31st bits)

Exponent: 11 bits (11 bits from 62nd to 52)

Fraction: 52 bits (52 bits from 51st to 0)

The true value of a 64-bit non-0 floating point is (python syntax ):

(-1) **Sign * 2 **(Exponent-1023) * (1 + Fraction)

Example:

A = 12.5

1. Solve the symbol bit

If a is greater than 0, the Sign is 0, which is expressed as: 0 in binary format.

2. Solving Order Codes

A Indicates binary: 1100.0

If the decimal point needs to be moved three places to the left, the Exponent is 1026 (1023 + 3), expressed in binary as: 10000000010

3. Solving valid numbers

If a valid number needs to be removed from the maximum implicit 1, the integer part of the valid number is: 100.

To convert decimal places to decimal places, use the following method to convert decimal places to decimal places: * 2. If an integer is obtained, the decimal places are: 1.

If the value is 0, the binary value of a can be expressed:

0100000000101001000000000000000000000000000000000000000000000000

That is: 0100 0000 0010 1001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

In hexadecimal notation: 0x4029000000000000

4. Restore the true value

Sign = bin(0) = 0Exponent = bin(10000000010) = 1026Fraction = bin(0.1001) = 2 ** (-1) + 2 ** (-4) = 0.5625

True Value:

(-1) **0 * 2 **(1026-1023) * (1 + 0.5625) = 12.5

64-bit floating point binary storage Parsing Code (c ++ ):

Https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/doubleTest1.cpp

Running effect:

[root@localhost t1]# ./doubleToBin1sizeof(double) : 8sizeof(long) : 8a = 12.500000showDouble : 0x 40 29 00 00 00 00 00 00UFP : 0,402,0b : 0x0showIEEE754 a = 12.500000showIEEE754 logLen = 3showIEEE754 c = 4620693217682128896(0x4020000000000000)showIEEE754 b = 0x4020000000000000showIEEE754 varTmp = 0x8000000000000showIEEE754 c = 0x8000000000000showIEEE754 i = 48 , a1 = 1.000000 , showIEEE754 c = 9000000000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 47 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 46 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 45 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 44 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 43 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 42 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 41 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 40 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 39 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 38 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 37 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 36 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 35 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 34 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 33 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 32 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 31 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 30 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 29 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 28 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 27 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 26 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 25 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 24 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 23 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 22 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 21 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 20 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 19 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 18 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 17 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 16 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 15 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 14 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 13 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 12 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 11 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 10 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 9 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 8 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 7 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 6 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 5 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 4 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 3 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 2 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 i = 1 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000showIEEE754 : 0x4029000000000000[root@localhost t1]#

 

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