Function to convert a number to binary

from math import log, floor

def largest_power_of_base_less_than(base, number):
    return int(floor(log(number, base)))

def to_binary(num):
    if num == 0:  # Log_2(0) = -infinity. Python dislikes infinity. We need to
        return '0'
    largest_power = largest_power_of_base_less_than(2, num)  # The largest integer <= log_2(num)
    current_power = largest_power  # We're going to change this one in the loop
    digits = []
    while current_power >= 0:
        if num >= (2 ** current_power):  # a**b means a^b (python uses ^ for binary xor instead of this)
            digits.append('1')  # This digit is a 1
            num = num - (2 ** current_power)  # Make the number smaller by the power of 2 we found
        else:
            digits.append('0')  # The current power of 2 isn't in our number, so this digit is a zero
        current_power = current_power - 1  # Move to the next smallest power of 2
    return ''.join(digits)  # This turns the list into a string. For example, ['1', '0', '1'] => '101'

def test():
    for num in range(0, 10):
        binary_version = to_binary(num)
        print("%s is %s in binary" % (num, binary_version))
        assert (num == int(binary_version, 2))
test()

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