# [Numpy-discussion] Custom floating point representation to IEEE 754 double

Oscar Benjamin oscar.j.benjamin at gmail.com
Tue Feb 25 18:12:46 EST 2014

```On 25 February 2014 11:08, Daniele Nicolodi <daniele at grinta.net> wrote:
> Hello,
>
> I'm dealing with an instrument that transfers numerical values through
> an RS232 port in a custom (?) floating point representation (56 bits, 4
> bits exponent and 52 bits significand).
>
> Of course I need to convert this format to a standard IEEE 754 double to
> be able to do anything useful with it.  I came up with this simple code:
>
>   def tofloat(data):
>       # 56 bits floating point representation
>       # 4 bits exponent
>       # 52 bits significand
>       d = frombytes(data)
>       l = 56
>       p = l - 4
>       e = int(d >> p) + 17
>       v = 0
>       for i in xrange(p):
>           b = (d >> i) & 0x01
>           v += b * pow(2, i - p + e)
>       return v
>
> where frombytes() is a simple function that assembles 7 bytes read from
> the serial port into an integer for easing the manipulation:
>
>   def frombytes(bytes):
>       # convert from bytes string
>       value = 0
>       for i, b in enumerate(reversed(bytes)):
>           value += b * (1 << (i * 8))
>       return value
>
> I believe that tofloat() can be simplified a bit, but except
> optimizations (and cythonization) of this code, there is any simpler way
> of achieving this?

My first approach would be that if you have an int and you want it as
bits then you can use the bin() function e.g.:
>>> bin(1234)
'0b10011010010'

You can then slice and reconstruct as ints with
>>> int('0b101', 2)
5

Similarly my first port of call for simplicity would be to just do
float(Fraction(mantissa, 2**exponent)). It doesn't really lend itself
to cythonisation but it should be accurate and easy enough to
understand.

Oscar

```