 Sencer H. -4 years ago 198
Python Question

# How to calculate mantissa in python when exponent hit to -127

I've got a location information in HEX string. I need to convert it into floating integer by IEEE-754 protocol.

So I wrote this code to find sign of the number, compute exponent and mantissa from binary representation of the given hexadecimal number.

``````def _calculte_mantissa(bin_number):
val = 1
bit_count = -1
bit_length = 0
while bit_length <= 22:
print bit_count, bit_length
val += int(bin_number[bit_length]) * 2**bit_count
bit_count -= 1
bit_length += 1
print val
return val

def convert_position(pos):
bin_pos = format(int(pos, 16), "0>32b")
sign = (-1)**int(bin_pos, 2)
exponent = int(bin_pos[1:9], 2) - 127
mantissa = _calculte_mantissa(bin_pos[9:])
position = sign * 2**exponent * mantissa
return position
``````

The problem is; If exponent is little than -126, say -127, the result is not correct. I check the result from this address, sign and exponent results are correct but mantissa result is different than mine.

I am missing something about the what that page is saying:

As a result, the mantissa has a value between 1.0 and 2. If the
exponent reaches -127 (binary 00000000), the leading 1 is no longer
used to enable gradual underflow.

Any way I know the problem is here but I can't figure out because of my insufficient English. Sencer H.
Answer Source

After suggestion of @Rudy Velthuis I figured out that I need to remove 1.0 and calculate with exponent -126 if exponent hit to -127. So the result is:

``````#! /usr/bin/env python
# -*- coding: utf-8 -*-
import sys

def _calculte_mantissa(bin_number, exponent):
val = 1 if exponent > -127 else 0
bit_count = -1
bit_length = 0
while bit_length <= 22:
val += int(bin_number\[bit_length\]) * 2**bit_count
bit_count -= 1
bit_length += 1
return val

def convert_ieee754(hex_val):
bin_pos = format(int(hex_val, 16), "0>32b")
sign = (-1)**int(bin_pos\[0\], 2)
_exponent = int(bin_pos\[1:9\], 2) - 127
mantissa = _calculte_mantissa(bin_pos\[9:\], _exponent)
exponent = _exponent if _exponent > -127 else -126
position = sign * 2**exponent * mantissa
return "Bin: %s - Sign: %s - Exponent: %s (%s) - Mantissa: %s - Posititon: %s" % (bin_pos, sign, exponent,
_exponent, mantissa, position)

if __name__ == "__main__":
argvs = sys.argv
print convert_ieee754(argvs\[1\])
sys.exit()
``````

https://github.com/RecNes/Python-IEEE754-Calculator-with-Denormalized-Values/blob/master/ieee754.py

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