Question

I’m trying to make a program to convert a number in any base to another base of the user’s choice. The code I have so far goes like this:

innitvar = float(raw_input("Please enter a number: "))
basevar = int(raw_input("Please enter the base that your number is in: "))
convertvar = int(raw_input("Please enter the base that you would like to convert to: "))

These are the data that I get from the user. The initial number, its initial base, and the base the user wants to convert to. As I understand it, I need to convert to base 10, and then to the desired base, specified by the user.

This is where I’m hitting a brick wall: I need to multiply the leftmost digit in the initial number by its initial base, and then add the next digit to the right, and then repeat until I hit the rightmost digit. I understand how to do this on paper, but I have no idea how to put it into Python code. I’m not sure how I would multiply the first number, and then add the next, nor do I understand how to let the program know when to stop performing this operation.

I’m not asking to have the program written for me, but I would like to be pointed in the right direction.

Thanks for your time!

Answer 1

This should be the first half of the answer to your problem. Can you figure out how to convert to a base?

# Create a symbol-to-value table.
SY2VA = {'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,
         'G': 16,
         'H': 17,
         'I': 18,
         'J': 19,
         'K': 20,
         'L': 21,
         'M': 22,
         'N': 23,
         'O': 24,
         'P': 25,
         'Q': 26,
         'R': 27,
         'S': 28,
         'T': 29,
         'U': 30,
         'V': 31,
         'W': 32,
         'X': 33,
         'Y': 34,
         'Z': 35,
         'a': 36,
         'b': 37,
         'c': 38,
         'd': 39,
         'e': 40,
         'f': 41,
         'g': 42,
         'h': 43,
         'i': 44,
         'j': 45,
         'k': 46,
         'l': 47,
         'm': 48,
         'n': 49,
         'o': 50,
         'p': 51,
         'q': 52,
         'r': 53,
         's': 54,
         't': 55,
         'u': 56,
         'v': 57,
         'w': 58,
         'x': 59,
         'y': 60,
         'z': 61,
         '!': 62,
         '"': 63,
         '#': 64,
         '$': 65,
         '%': 66,
         '&': 67,
         "'": 68,
         '(': 69,
         ')': 70,
         '*': 71,
         '+': 72,
         ',': 73,
         '-': 74,
         '.': 75,
         '/': 76,
         ':': 77,
         ';': 78,
         '<': 79,
         '=': 80,
         '>': 81,
         '?': 82,
         '@': 83,
         '[': 84,
         '\\': 85,
         ']': 86,
         '^': 87,
         '_': 88,
         '`': 89,
         '{': 90,
         '|': 91,
         '}': 92,
         '~': 93}

# Take a string and base to convert to.
# Allocate space to store your number.
# For each character in your string:
#     Ensure character is in your table.
#     Find the value of your character.
#     Ensure value is within your base.
#     Self-multiply your number with the base.
#     Self-add your number with the digit's value.
# Return the number.

def str2int(string, base):
    integer = 0
    for character in string:
        assert character in SY2VA, 'Found unknown character!'
        value = SY2VA[character]
        assert value < base, 'Found digit outside base!'
        integer *= base
        integer += value
    return integer

Here is the second half of the solution. By using these two functions, converting bases is very easy to do.

# Create a value-to-symbol table.
VA2SY = dict(map(reversed, SY2VA.items()))

# Take a integer and base to convert to.
# Create an array to store the digits in.
# While the integer is not zero:
#     Divide the integer by the base to:
#         (1) Find the "last" digit in your number (value).
#         (2) Store remaining number not "chopped" (integer).
#     Save the digit in your storage array.
# Return your joined digits after putting them in the right order.

def int2str(integer, base):
    array = []
    while integer:
        integer, value = divmod(integer, base)
        array.append(VA2SY[value])
    return ''.join(reversed(array))

After putting it all together, you should end up with the program below. Please take time to figure it out!

innitvar = raw_input("Please enter a number: ")
basevar = int(raw_input("Please enter the base that your number is in: "))
convertvar = int(raw_input("Please enter the base that you would like to convert to: "))

# Create a symbol-to-value table.
SY2VA = {'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,
         'G': 16,
         'H': 17,
         'I': 18,
         'J': 19,
         'K': 20,
         'L': 21,
         'M': 22,
         'N': 23,
         'O': 24,
         'P': 25,
         'Q': 26,
         'R': 27,
         'S': 28,
         'T': 29,
         'U': 30,
         'V': 31,
         'W': 32,
         'X': 33,
         'Y': 34,
         'Z': 35,
         'a': 36,
         'b': 37,
         'c': 38,
         'd': 39,
         'e': 40,
         'f': 41,
         'g': 42,
         'h': 43,
         'i': 44,
         'j': 45,
         'k': 46,
         'l': 47,
         'm': 48,
         'n': 49,
         'o': 50,
         'p': 51,
         'q': 52,
         'r': 53,
         's': 54,
         't': 55,
         'u': 56,
         'v': 57,
         'w': 58,
         'x': 59,
         'y': 60,
         'z': 61,
         '!': 62,
         '"': 63,
         '#': 64,
         '$': 65,
         '%': 66,
         '&': 67,
         "'": 68,
         '(': 69,
         ')': 70,
         '*': 71,
         '+': 72,
         ',': 73,
         '-': 74,
         '.': 75,
         '/': 76,
         ':': 77,
         ';': 78,
         '<': 79,
         '=': 80,
         '>': 81,
         '?': 82,
         '@': 83,
         '[': 84,
         '\\': 85,
         ']': 86,
         '^': 87,
         '_': 88,
         '`': 89,
         '{': 90,
         '|': 91,
         '}': 92,
         '~': 93}

# Take a string and base to convert to.
# Allocate space to store your number.
# For each character in your string:
#     Ensure character is in your table.
#     Find the value of your character.
#     Ensure value is within your base.
#     Self-multiply your number with the base.
#     Self-add your number with the digit's value.
# Return the number.

integer = 0
for character in innitvar:
    assert character in SY2VA, 'Found unknown character!'
    value = SY2VA[character]
    assert value < basevar, 'Found digit outside base!'
    integer *= basevar
    integer += value

# Create a value-to-symbol table.
VA2SY = dict(map(reversed, SY2VA.items()))

# Take a integer and base to convert to.
# Create an array to store the digits in.
# While the integer is not zero:
#     Divide the integer by the base to:
#         (1) Find the "last" digit in your number (value).
#         (2) Store remaining number not "chopped" (integer).
#     Save the digit in your storage array.
# Return your joined digits after putting them in the right order.

array = []
while integer:
    integer, value = divmod(integer, convertvar)
    array.append(VA2SY[value])
answer = ''.join(reversed(array))

# Display the results of the calculations.
print answer