Because why not.

8bit_adder.py

_hex = {'0':0, '1':1, '2':2, '3':3, '4':4, '5':5,
        '6':6, '7':7, '8':8, '9':9, 'A':10, 'B':11,
        'C':12, 'D':13, 'E':14, 'F':15}

def bit(n1, n2):    
    if str(n1).upper() not in _hex:
        raise ValueError('Invalid n1')
    elif str(n2).upper() not in _hex:
        raise ValueError('Invalid n2')

    A = _hex[str(n1).upper()]
    B = _hex[str(n2).upper()]

    return ((16 * A) % 241) + (1 * B) % 16

def adder(A, B, C = 0):
    F1 = bit(A[0], A[1])
    F2 = bit(B[0], B[1])

    return ((F1 + F2) % 256) + C

def _16bit_unsigned(b1, b2):
    if not isinstance(b1, list):
        raise ValueError('Invalid b1')
    elif not isinstance(b2, list):
        raise ValueError('Invalid b2')

    A = bit(b1[0], b1[1]) + 1
    B = bit(b2[0], b2[1]) + 1
    C = (A * B) - 1

    return C % (256 ** 2)

def _32bit_unsigned(b1, b2, b3, b4):
    if not isinstance(b1, list):
        raise ValueError('Invalid b1')
    elif not isinstance(b2, list):
        raise ValueError('Invalid b2')
    elif not isinstance(b3, list):
        raise ValueError('Invalid b3')
    elif not isinstance(b4, list):
        raise ValueError('Invalid b4')

    A = bit(b1[0], b1[1]) + 1
    B = bit(b2[0], b2[1]) + 1
    C = bit(b3[0], b3[1]) + 1
    D = bit(b4[0], b4[1]) + 1
    E = (A * B * C * D) - 1

    return E % (256 ** 4)

def _64bit_unsigned(b1, b2, b3, b4, b5, b6, b7, b8):
    if not isinstance(b1, list):
        raise ValueError('Invalid b1')
    elif not isinstance(b2, list):
        raise ValueError('Invalid b2')
    elif not isinstance(b3, list):
        raise ValueError('Invalid b3')
    elif not isinstance(b4, list):
        raise ValueError('Invalid b4')
    elif not isinstance(b5, list):
        raise ValueError('Invalid b5')
    elif not isinstance(b6, list):
        raise ValueError('Invalid b6')
    elif not isinstance(b7, list):
        raise ValueError('Invalid b7')
    elif not isinstance(b8, list):
        raise ValueError('Invalid b8')

    A = bit(b1[0], b1[1]) + 1
    B = bit(b2[0], b2[1]) + 1
    C = bit(b3[0], b3[1]) + 1
    D = bit(b4[0], b4[1]) + 1
    E = bit(b5[0], b5[1]) + 1
    F = bit(b6[0], b6[1]) + 1
    G = bit(b7[0], b7[1]) + 1
    H = bit(b8[0], b8[1]) + 1
    I = (A * B * C * D * E * F * G * H) - 1

    return I % (256 ** 8)