Base Conversion

Most of the modern world uses a base-10 number system. It's the easiest to work with. However, when it comes to computer systems, we use a few different number systems too. Base-2, or binary, is the basis of data storage and transmission; a bit is either on or off. We also use Base-8, or octal; each byte contains 8 bits. Last but not least is Base-16, or hexadecimal.

Under some circumstances, we might need to convert between these different number systems. ASP provides a pathetic two functions for this purpose: hex(), which converts from base-10 (decimal) to base-16 (hexadecimal), and oct() which converts from decimal to octal. PHP provides equivalent functions dechex() and decoct(), as well as additional functions decbin() for converting from decimal to binary, bindec() for converting from binary to decimal, hexdec() for converting from hexadecimal to decimal, and octdec() for converting from octal to decimal.

It would be nice to extend ASP to support these four additional functions. When I started doing that, I noticed a pattern in the formulae. All the functions that converted from decimal were fairly similar, and all the functions that converted to decimal were also fairly similar. So I abstracted the calculations out into their own functions and simplified my code.

ASP

1. ' Convert from binary to decimal.
2. function bindec(bin)
3.     bindec = toDecimal(bin, 2)
4. end function
6. ' Convert from decimal to binary
7. function decbin(dec)
8.     decbin = fromDecimal(dec, 2)
9. end function
11. ' Convert from decimal to hexadecimal.
12. function dechex(dec)
13.     ' Assume that built-in hex() function is faster.
14.     dechex = hex(dec)
15. end function
17. ' Convert from decimal to octal.
18. function decoct(dec)
19.     ' Assume that built-in oct() function is faster.
20.     decoct = oct(dec)
21. end function
23. ' Convert from hexadecimal to decimal.
24. function hexdec(hex)
25.     hexdec = toDecimal(hex, 16)
26. end function
28. ' Convert from octal to decimal.
29. function octdec(oct)
30.     octdec = toDecimal(oct, 8)
31. end function

Before we get into the underlying fromDecimal() and toDecimal() functions, some things need to be said. The lowest possible base is 2, so if the user tries to specify a base smaller than 2, we will change it to 2. Likewise, there is a practical upper limit of base 36. Beyond that, things get more complicated, so any base higher than 36 will be changed to 36 to prevent the function from going out of bounds and returning bad data.

ASP

1. function toDecimal(value, radix)
2.     dim result
3.     dim digit
5.     result = 0
7.     ' Prevent radix from going out of bounds.
8.     if radix < 2 then
9.         radix = 2
10.     elseif radix > 36 then
11.         radix = 36
12.     end if
14.     for i = 1 to Len(value)
15.         digit = Mid(value, i, 1)
17.         ' Convert letters to numbers.
18.         if not isNumeric(digit) then
19.             ' The letter A in any base is equal to 10 in decimal.
20.             ' The ASCII value of A is 65, so subtract 55 from the ASCII value to obtain the decimal value.
21.             digit = Asc(UCase(digit)) - 55
22.         else
23.             digit = CInt(digit)
24.         end if
26.         ' Return zero if any digit is out of bounds for the radix.
27.         if digit >= radix then
28.             result = 0
29.             exit for
30.         end if
32.         result = result + (digit * radix ^ (Len(value) - i))
33.     next
35.     toDecimal = result
36. end function
38. function fromDecimal(value, radix)
39.     dim result
40.     dim digit
42.     result = 0
44.     ' Prevent radix from going out of bounds.
45.     if radix < 2 then
46.         radix = 2
47.     elseif radix > 36 then
48.         radix = 36
49.     end if
51.     ' Check for invalid input.
52.     if isNumeric(value) then
53.         ' Inputted value appears to be base 10. OK to proceed.
54.         do until value = 0
55.             digit = value Mod radix
57.             if digit > 9 then
58.                 digit = Chr(digit + 55)
59.             end if
61.             result = CStr(digit) & result
62.             value = value \ radix
63.         loop
64.     else
65.         ' Inputted value was NOT base 10.
66.         result = 0
67.     end if
69.     fromDecimal = result
70. end function

It would be even better if we could easily convert between two bases where neither one is decimal. Also, it would be nice to have a unified interface. We can achieve both with one function, base_convert(), which is also present in PHP.

ASP

1. function base_convert(value, sourceRadix, targetRadix)
2.     if sourceRadix = targetRadix then
3.         ' If source radix and target radix are equal, don't waste time converting.
4.         baseConv = value
5.     elseif sourceRadix = 10 then
6.         ' If source radix is decimal, skip converting to decimal.
7.         baseConv = fromDecimal(value, targetRadix)
8.     elseif targetRadix = 10 then
9.         ' If target radix is decimal, skip converting from decimal.
10.         baseConv = toDecimal(value, sourceRadix)
11.     else
12.         ' Convert to decimal, and then from decimal.
13.         baseConv = fromDecimal(toDecimal(value, sourceRadix), targetRadix)
14.     end if
15. end function

I leave you with the following potential exercises:

• From base 37 to 62, the lowercase letters of the Latin alphabet are used, but special handling would need to be added for them. The ASCII value for Z is 90. The ASCII value for a is 97. There are six other characters in between.
• Base64 encoding begins with the uppercase letters A-Z, followed by a-z, followed by 0-9, followed by + and /. If you want to add Base64 support, separate functions would be wise, but could still be tied into the base_convert() wrapper.