def division_op(number1, number2, base):
"""
This function performs the division of two numbers ([number1] and [number2])
in base [base]
:param number1: a string representing the first number in base [base]
:param number2: a string representing the second number in base [base] having one digit
:param base: the base in which the numbers are represented and the division is done
:return: two strings representing the quotient and reminder of the division between [number1] and [number2]
Raises a ValueError if [number2] if 0 or if is has more than one digit
"""
if number2 == '0':
raise ValueError("Cannot divide by 0")
if len(number2) != 1:
raise ValueError("Invalid operand")
if base == 10:
return str(int(number1) // int(number2)), str(
int(number1) % int(number2))
else:
max_len = len(number1)
result = ""
num_to_div_str = ""
# we do the division looping through the number
for i in range(max_len):
num_to_div_str += number1[i]
if len(num_to_div_str) == 1:
if get_number_from_character(
number1[i]) < get_number_from_character(
number2[0]):
if i != 0:
result += '0'
continue
num_to_div = to_base_10(num_to_div_str, base)
div = get_number_from_character(number2[0])
last_digit = num_to_div // div
result = result + get_character_from_number(last_digit)
if num_to_div % div != 0:
num_to_div_str = get_character_from_number(num_to_div %
div)
else:
num_to_div_str = ""
# if the reminder is "" then it is 0
if num_to_div_str == "":
num_to_div_str = "0"
# if the result is "" we return 0
if result == "":
return '0', num_to_div_str
else:
return result, num_to_div_str
def addition(number1, number2, base):
"""
This function performs the addition of two numbers ([number1] and [number2])
in base [base]
:param number1: a string representing the first number in base [base]
:param number2: a string representing the second number in base [base]
:param base: the base in which the numbers are represented and the addition is done
:return: a string representing the sum of [number1] and [number2]
"""
if base == 10: # if the numbers are in base 10 we do
return str(
int(number1) +
int(number2)) # the normal addition of two numbers in base 10
else:
reminder = 0
if len(number1) < len(
number2): # compare the length of the numbers
aux = number1 # and put the longest in number1
number1 = number2
number2 = aux
min_len = len(number2)
max_len = len(number1)
diff = max_len - min_len
result = ""
# go through the numbers from last digit to the first digit of the shortest and do the addition
for i in range(min_len - 1, -1, -1):
last_digit = (get_number_from_character(number1[i + diff]) +
get_number_from_character(number2[i]) +
reminder) % base
result = result + get_character_from_number(last_digit)
reminder = (get_number_from_character(number1[i + diff]) +
get_number_from_character(number2[i]) +
reminder) // base
# if the numbers had the same length we put the reminder as the first digit if it is not 0
if max_len == min_len and reminder != 0:
result = result + get_character_from_number(reminder)
# if they had not the same length we add the digits of the longest and add the reminder to them
elif max_len > min_len:
for i in range(max_len - min_len - 1, -1, -1):
last_digit = (get_number_from_character(number1[i]) +
reminder) % base
result = result + get_character_from_number(last_digit)
reminder = (get_number_from_character(number1[i]) +
reminder) // base
# reverse the digits of the result to obtain the correct number
result = result[::-1]
return result
def multiplication(number1, number2, base):
"""
This function performs the multiplication of two numbers ([number1] and [number2])
in base [base]
:param number1: a string representing the first number in base [base]
:param number2: a string representing the second number in base [base] having one digit
:param base: the base in which the numbers are represented and the multiplication is done
:return: two strings representing product of [number1] and [number2]
Raises a ValueError if [number2] is 0 or if is has more than one digit
"""
if base == 10:
return str(int(number1) * int(number2))
else:
# find the number having one digit
if len(number1) == 1 and len(number2) > 1:
to_mul = number1
to_be_mul_int = number2
else:
to_mul = number2
to_be_mul_int = number1
reminder = 0
max_len = len(to_be_mul_int)
result = ""
if len(to_mul) != 1:
raise ValueError("Invalid operand")
else:
for i in range(max_len - 1, -1, -1):
last_digit = (get_number_from_character(to_be_mul_int[i]) *
get_number_from_character(to_mul[0]) +
reminder) % base
result = result + get_character_from_number(last_digit)
reminder = (get_number_from_character(to_be_mul_int[i]) *
get_number_from_character(to_mul[0]) +
reminder) // base
# if the reminder is not 0 then we add it at the beginning of the result
if reminder != 0:
result += get_character_from_number(reminder)
# reverse the digits to get the correct number
result = result[::-1]
if result[0] == '0':
return '0'
else:
return result
def successive_divisions(number, source_base, destination_base):
"""
It converts a number from base [source_base] in base [destination_base] using the
successive divisions algorithm.
:param number: string representing number in base [source_base]
:param source_base: the source base
:param destination_base: the destination base
:return: converted number
Raises ValueError if the number contains digits >= than the source_base
"""
for x in number:
if get_number_from_character(x) >= source_base:
raise ValueError("Invalid number in source base")
quotient = number
result = ""
destination_base = get_character_from_number(destination_base)
while quotient != "0":
quotient, reminder = Operations.division_op(
quotient, destination_base, source_base)
result += reminder
result = result[::-1]
return result
def substitution_method(number, source_base, destination_base):
"""
It converts a number from base [source_base] in base [destination_base] using the
substitution algorithm.
:param number: string representing number in base [source_base]
:param source_base: the source base [2-16]
:param destination_base: the destination base [2-16]
:return: converted number
Raises ValueError if the number contains digits >= than the source_base
"""
for x in number:
if get_number_from_character(x) >= source_base:
raise ValueError("Invalid number in source base")
result = "0"
exp = len(number) - 1
for digit in number:
current_power = "1"
for i in range(exp):
current_power = Operations.multiplication(
current_power, get_character_from_number(source_base),
destination_base)
current_power = Operations.multiplication(current_power, digit,
destination_base)
result = Operations.addition(result, current_power,
destination_base)
exp -= 1
return result
def rapid_conversions(number, source_base, destination_base):
"""
It converts a number from base [source_base] in base [destination_base] using the
rapid conversions algorithm.
:param number: string representing number in base [source_base]
:param source_base: the source base [2, 4, 8, or 16]
:param destination_base: the destination base [2, 4, 8, or 16]
:return: converted number
Raises ValueError if the bases are not [2, 4, 8 or 16] or if the number contains digits >= than the source_base
"""
allowed_bases = [2, 4, 8, 16]
if source_base not in allowed_bases or destination_base not in allowed_bases:
raise ValueError("Invalid source base for rapid conversions")
for x in number:
if get_number_from_character(x) >= source_base:
raise ValueError("Invalid number in source base")
pow_2_source = int(math.log2(source_base))
pow_2_destination = int(math.log2(destination_base))
bits = []
for i in range(len(number) - 1, -1, -1):
digit = get_number_from_character(number[i])
for j in range(pow_2_source):
bits.append(digit % 2)
digit //= 2
while len(bits) % pow_2_destination != 0:
bits.append(0)
result = ""
for i in range(0, len(bits), pow_2_destination):
digit = get_character_from_number(
sum([bits[i + j] * (1 << j)
for j in range(pow_2_destination)]))
result += digit
result = result[::-1]
return result
def subtraction(number1, number2, base):
"""
This function performs the subtraction of two numbers ([number1] and [number2])
in base [base]
:param number1: a string representing the first number in base [base]
:param number2: a string representing the second number in base [base]
:param base: the base in which the numbers are represented and the subtraction is done
:return: two strings representing difference between [number1] and [number2]
Raises a ValueError if [number2] is greater than [number1]
"""
if base == 10:
return str(int(number1) - int(number2))
else:
if compare_int_numbers(number1, number2) == -1:
raise ValueError("The subtrahend is greater than minuend")
reminder = 0
if len(number1) < len(number2):
raise ValueError("The subtrahend is greater than minuend")
else:
min_len = len(number2)
max_len = len(number1)
diff = max_len - min_len
result = ""
# go through the numbers from last digit to the first digit of the shortest and do the subtraction
for i in range(min_len - 1, -1, -1):
minuend = get_number_from_character(number1[i + diff])
sub = get_number_from_character(number2[i])
if minuend < sub + reminder:
last_digit = minuend + base - sub - reminder
reminder = 1
else:
last_digit = minuend - sub - reminder
reminder = 0
result = result + get_character_from_number(last_digit)
if max_len == min_len and reminder != 0:
result = result + get_character_from_number(reminder)
# if the first number is longer than the second we put its digits athe the beginning
# of the result subtracting the reminder
elif max_len > min_len:
for i in range(max_len - min_len - 1, -1, -1):
if get_number_from_character(number1[i]) < reminder:
last_digit = get_number_from_character(
number1[i]) + base - reminder
reminder = 1
else:
last_digit = get_number_from_character(
number1[i]) - reminder
reminder = 0
result = result + get_character_from_number(last_digit)
# reverse the digits to get the correct number
result = result[::-1]
if result != "0":
result = result.lstrip("0")
return result