Integer to "binary string"?

[Dan Bishop]

Gustaf Liljegren <gustafl at algonet.se> wrote in message news:<Xns92E5D08902B0Fgustafl at 195.100.94.182>...
> I'm writing a short program to help me understand certain concepts of the 
> character encoding UTF-16. The script should be able to encode integers to 
> strings of ones and zeros, to illustrate what happens during serialization.
> 
> I was hunting for a function to convert integers to these strings and vice 
> versa, but found none. Then I hunted on Google and found:

A binary to integer conversion can be done with int(bitString, 2). 
There's a standard function to convert the other way, but right now I
don't remember what it's called.

> def bin(i):
>      s = ''
>      while i:
>          s = (i & 1 and '1' or '0') + s
>          i >>= 1
>      return s or '0'
> 
> This works, but I don't understand it. Can anyone explain what happens on 
> the three last rows? Also, can you show how to write a similar function for 
> decoding?

The code is (imho) obfuscated, so I'll rewrite it to increase clarity
by replacing the and's and or's with if's and else's, using the
short-circuiting property of "and" and "or".

def bin(i):
   s = ''
   while i:
      if i & 1:
         s = '1' + s
      else:
         s = '0' + s
      i >>= 1
   if s:
      return s
   else:
      return '0'


> if i & 1:

& is a bitwise AND operator, and the bitmask 1 corresponds to the last
bit of the number.  If this bit is nonzero (i.e., 1), a '1' is added
to the s; otherwise, a '0' is added.  (Why is it added to the front
instead of the end?  We'll see later.)

> i >>= 1

Right shift by one bit; throw away the last bit of of i.

The recursive definition of an int-to-binary string conversion is

(all but the last bit of i) + str(last bit of i)
= bin(i >> 1) + str(i & 1)

This iterative version calculates these terms in reverse order, which
is why the string s is built in reverse order.

> return s or '0'

If s is true (i.e., len(s) > 0), then s is returned.  Otherwise, '0'
is returned.