As you may know, instead of using all of the natural numbers, binary uses only 0 and 1's. As quoted by Wikipedia "When the symbols for the first digit are exhausted, the next-higher digit (to the left) is incremented," and then is released to the next 0. Example:

In decimal system numbers run as thus:

001, 002, 003, 004 (As the number on the far right ends it precedes to the next number)

008, 009, 010 (And therefor as the numbers increase it addes a 0 to the end)

In binary it follows as thus:

000, 001, 010, 011 (In binary it runs with virtually the same effect, except it uses only 0's and 1's.)

So the next one would be 100, 101, etc.

Here is the relation between the hexadecimal system:

Hex Dec Binary

0 0 0000

1 1 0001

2 2 0010

3 3 0011

Hex Dec Binary

4 4 0100

5 5 0101

6 6 0110

7 7 0111

Hex Dec Binary

8 8 1000

9 9 1001

A 10 1010

B 11 1011

Hex Dec Binary

C 12 1100

D 13 1101

E 14 1110

F 15 1111

To convert a hexadecimal number to it's decimal equivalent - according to wikipedia - "multiply the decimal equivalent of each hexadecimal digit by the corresponding power of 16 and add the resulting values:"

C0E716 = (12 × 163) + (0 × 162) + (14 × 161) + (7 × 160) = (12 × 4096) + (0 × 256) + (14 × 16) + (7 × 1) = 49,38310

Whilst converting to the octal system it would follow as thus:

Octal Binary

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

This is due because octal uses a radix of 8.

Anything else to add?