How to converting floating point number

Question

A converting between the decimal to single-precision floating,but i intro to this,so did any useful references or any summarize can help?

Thousand Thanks!

so,the python function will be like

require a user to select convert from decimal to to floating point number or floating point number convert to decimal.
input value
will show the step such as

i. Sign

ii. Exponent

iii. Mantissa
return the result.

below is the example i searched from internet but this is 64bit so,how change it to 32bit and show the step when converting?

    import struct

getBin = lambda x: x > 0 and str(bin(x))[2:] or "-" + str(bin(x))[3:]

def floatToBinary64(value):
    val = struct.unpack('Q', struct.pack('d', value))[0]
    return getBin(val)

def binaryToFloat(value):
    hx = hex(int(value, 2))   
    return struct.unpack("d", struct.pack("q", int(hx, 16)))[0]

# floats are represented by IEEE 754 floating-point format which are 
# 64 bits long (not 32 bits)

# float to binary
binstr = floatToBinary64(19.5)
print('Binary equivalent of 19.5:')
print(binstr + '\n')

# binary to float
fl = binaryToFloat(binstr)
print('Decimal equivalent of ' + binstr)
print(fl)

Could you clarify the formats (and Python types) of the inputs and outputs? Some examples might help, too. — Mark Dickinson
– Mark Dickinson, Commented Jul 8, 2019 at 19:57
It makes not much sense to convert a float to a decimal. Since due to rounding errors, the values will not be very accurate. — willeM_ Van Onsem
– willeM_ Van Onsem, Commented Jul 8, 2019 at 19:59
@WillemVanOnsem i had create a example link that with C language,but i am looking for python,thanks. — step
– step, Commented Jul 8, 2019 at 20:07

Stef · Accepted Answer · 2019-07-09 07:33:16Z

0

Using the answers to this SO question we get:

import struct

def floatToBinary32(value):
    return ''.join(f'{c:0>8b}' for c in struct.pack('!f', value))

def binaryToFloat(value):
    hx = hex(int(value, 2))   
    return struct.unpack("f", struct.pack("l", int(hx, 16)))[0]

# float to binary
fl0 = 19.5
binstr = floatToBinary32(fl0)
print(f'Binary equivalent of {fl0}: {binstr}')

# binary to float
fl1 = binaryToFloat(binstr)
print(f'Decimal equivalent of      {binstr}: {fl1}')

print(f'\nSign     ( 1 bit ) = {binstr[0]}\nExponent ( 8 bits) = {binstr[1:9]}\nMantissa (23 bits) = {binstr[9:]}')

assert fl0 == fl1

Output:

Binary equivalent of 19.5: 01000001100111000000000000000000
Decimal equivalent of      01000001100111000000000000000000: 19.5

Sign     ( 1 bit ) = 0
Exponent ( 8 bits) = 10000011
Mantissa (23 bits) = 00111000000000000000000

Please note however that, as already pointed out in the comments above, such conversions are not exact as you can see when using for example fl0 = 0.1. This also shows that python (CPython) uses 64 bit floats (implemented using double in C).

edited Jul 9, 2019 at 7:33

answered Jul 9, 2019 at 6:37

Stef

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1 Comment

step Over a year ago

hi,thanks for helping me about this question. i check on this have some problem with return struct.unpack("f", struct.pack("l", int(hx, 16)))[0],but i had modified, and it worked now. A thousand thanks again! :)

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