frac_to_bin.py

BASE = 2

def to_binary(a, b):
    """
    Converts a fraction (a/b) to a binary representation.

    Parameters:
    a (int): The numerator of the fraction.
    b (int): The denominator of the fraction.

    Returns:
    tuple: A tuple containing two elements. The first element is the period length,
           and the second element is the binary representation of the fraction.
           If the fraction is a repeating decimal, the binary representation will
           contain 'r' to indicate the repeating part.
    """
    temp = a
    chk = [a]
    ret = ''
    while True:
        temp *= BASE
        if temp > b:
            temp -= b
            ret += '1'
        elif temp == b:
            ret += '1'
            return (0, '.' + ret)
        else:
            ret += '0'
        chk.append(temp)
        if (len(chk) - len(set(chk))) != 0:
            for i in range(len(chk) - 1):
                if chk[i] == chk[-1]:
                    ret = ret[:i] + 'r' + ret[i:]
            break
    return len(ret[ret.index('r'):]) - 1, '.' + ret


nu = int(input('분자: '))
de = int(input('분모: '))

period_length, binary_repr = to_binary(nu, de)
print(f"{nu}/{de}, {(period_length, binary_repr)}")