Octal and Hex

Binary math is just as simple as decimal math, so is Octal and Hexidecimal.

Name	Base	Digits
Binary Octal Decimal Hexidecimal	2 8 10 16	0 1 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 A B C D E F

Converting between bases is easy. To convert from Decimal to anything else you must first convert it to binary. This is taught in the first section of notes and will not be discussed here.

So why use Hexidecimal or Octal numbers? Well the reason we use Binary first off is because that is what computers use, and I can communicate quite easilly with it if I know binary. Lets use a perfectly random, made up example.


Example:
         1101001101010100
                             Lets rewite that as
         1101 0011 0101 0100   
                             So it is easier to view.
                             Now lets decode it....

         Digits 
          1       Direct/Indirect addressing
          2- 4    Operation
          5- 8    First Value
          9-12    Second Value
         13-16    Destination

So this may mean....
Using direct accessing mode, add register 3 to 5 and store the value in register 4.

So looking at the number 1101001101010100 its really hard to tell what is ment, however if I write that same number in Hexidecimal, I get D354 which is a lot easier to read and tells me a few things,
D=indirect add
3=first value
5=second value
4=destination
It is very easy to read and to translate. Some computers are designed around an Octal base (3 digit binary number) or a hexidecimal base (4 digit binary number) so it is advantageous to know both octal and hexidecimal conversion.

Decimal	Binary	Octal	Hexidecimal
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17	00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001	000 001 002 003 004 005 006 007 010 011 012 013 014 015 016 017 020 021	00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10 11

Doing conversions is extreamly simple.
To convert from Binary to Octal divide your binary number into groups of 3, starting from the right side of the number. So, for example, 1010110111101 => 1 010 110 111 101. Second, now take each group of 3 and insert its Octal representation. 1 010 110 111 101 => 12675. So our nunber is 12675 in octal.

To convert from Binary to Hexidecimal divide your binary number into groups of 4, starting from the right side of the number. So, for example, 1010110111101 => 1 0101 1011 1101. Second, now take each group of 4 and insert its Hex representation. 1 0101 1011 1101 => 15BD. So our nunber is 15BD in hex.

Numbers are typically writen as follows:

     Decimal: 56
     Binary : 0111000b
     Octal  : x70  or 38o
     Hex    : 0x38 or 38h

Ok, so now we can convert between Decimal, Binary, Octal and Hexidecimal. When converting decimal places, however, you start from the left and divide the binary number into groups of 3 or 4. So basiclly you start at the decimal point and move out.