float.py

import struct

def display_float(x):
    """ prints 64 bits in the representation of the float x """
    if isinstance(x, float):
        q, = struct.unpack('Q', struct.pack("d", x))
        full_bin = "{:064b}".format(q)
        sign= full_bin[0]
        exponent_plus = full_bin[1:12]
        fraction=full_bin[12:]
        return sign + " " + exponent_plus + " " + fraction
    else:
        return None

def show_fractions_between_one_and_two():
    for i in range(1, 54):
        x = sum([ 1/(2.**j) for j in range(i) ])
        print(display_float(x), "-", x)