This turns any positive integer into its binary representation, but as an integer, so it's not really binary. Just a fun thing I figured out.

binarise.js

var p = Math.log(20)/Math.log(2) - 1;

function binarise(x)
{
    if(x === 0)
    {
        return 0;
    }
    
    if(x === 1)
    {
        return 1;
    }

    if(x < 0)
    {
        throw 'not implemented for negative numbers';
    }
    
    if(x > 0 && x < 1)
    {
        throw 'not implemented for non-integers';
    }

    if ((x & (x - 1)) != 0)
    {
        var bit = prevIntPoT(x);
        var leftover = x - bit;

        return binarise(bit) + binarise(leftover);
    }

    var result = Math.floor(Math.pow(x, p));

    if(result == Number.POSITIVE_INFINITY)
    {
        throw 'The input is too big.'
    }

    return result;
}

function prevIntPoT(x)
{  
    return 2**(x.toString(2).length - 1);
}

rounding errors mean that problems occur after 32767