Question

This is about how to do number conversion between binary to octal, octal to hexadecimal, binary to hexadecimal.. ( in all these decimal is no where there, either in source or destination )

Whenever decimal is involved either in source or destination i have a general methodology as,

• if decimal is source, do the mod operation of that number with the base of destination. ( and continue the same way, and get the result ),
  Example: convert decimal 20 to octal
  • 20 mod 8 = 4
    • 2 = 2

So it is 24 in Octal. This way you can do for anything ( binary, hex ) from Decimal.

• if decimal is destination, do the multiplication operation with the source’s base from 0 to N which starts from left to right. And add up to get the decimal.
  Example: convert binary 1010 to decimal
  • 0 : 0 x 2**0 = 0
    • 1 : 1 x 2**1 = 2
      • 0 : 0 x 2**2 = 0
        • 1: 1 x 2**3 = 8

The sum is 10 in Decimal. This way you can do for anything ( octal, hex ) to decimal.

Questions
Is there any similar general logic, which i can use for conversion between octal, hex and binary ?

Hope the above is clear.. Else let me know.

Answer 1

The conversion between binary and either octal or hex is even easier than decimal. Just break the binary digits up into groups of 3 or 4 (depending on oct or hex), then convert each group to a digit. (If you don’t have a multiple of 3 or 4 binary digits, just left-pad the number with zeros.)

Example:

111101111010 binary
1111 0111 1010
   F    7    A
           F7A hex

111101111010
111 101 111 010
  7   5   7   2
           7572 oct

Converting back is just the opposite. Each digit in octal or hex gets converted directly to either 3 or 4 binary digits.