After a little discussion with some users in IRC, I was asked on how I teach the conversation from hex to binary to decimal. So I've decided to post everything here along the lines that I usually teach in class.

First, let's look at binary. It is merely a 1 (on) or 0 (off). We see binary used in a variety ways from permissions (in unix) to tcp/ip addresses to attribute settings. (space out the bit so that a decimal appears under each 0)

0 0 0 0 0 0 0 0

128 64 32 16 8 4 2 1

So if my binary was like below:

0 1 1 0 1 1 0 0

128 64 32 16 8 4 2 1

This means that the bits 64, 32, 8, 4 are turned on totalling a value of 108 (64+32+8+4).

If you have to go beyond the 8 bits (the examples above are 8 bits as found in IPv4 addressing aka 32bit addressing --> 4x8bits), just continue doubling the numbers. So if I had to go to 12 bits (aka Fat12) I would have:

0 0 0 0 0 0 0 0 0 0 0 0

2048 1024 512 256 128 64 32 16 8 4 2 1

And so on.

Simple, eh? Now, how about Hex? Well Hex aka Hexadecimal is a "base-16" numbering system. Binary is a "base-2" (based on 2 digits) and decimal is "base-10" (based on 10 digits).

If I was to count in binary and decimal it would be:

Binary = Decimal

0000 = 0

0001 = 1

0010 = 2

0011 = 3

0100 = 4

0101 = 5

0110 = 6

0111 = 7

1000 = 8

1001 = 9

1010 = 10

1011 = 11

1100 = 12

1101 = 13

1110 = 14

1111 = 15

So, now I can count easily from 0 to 15. Oh. Interesting. 16 digits. ;) We'll add the hex to the digit now.

Binary = Decimal = Hexadecimal

0000 = 0 = 0

0001 = 1 = 1

0010 = 2 = 2

0011 = 3 = 3

0100 = 4 = 4

0101 = 5 = 5

0110 = 6 = 6

0111 = 7 = 7

1000 = 8 = 8

1001 = 9 = 9

1010 = 10 = A

1011 = 11 = B

1100 = 12 = C

1101 = 13 = D

1110 = 14 = E

1111 = 15 = F

So now I can go from binary to decimal to Hex. This little chart is easy to setup and handy to have. Once you have this the rest is straightforward. An example:

0 1 1 0 1 0 1 0 1 1 1 0

2048 1024 512 256 128 64 32 16 8 4 2 1

Notice that there are 12 bits. Seperate your bits into groups of 4 like so:

0 1 1 0 1 0 1 0 1 1 1 0

And do the hex for each (hex is easier than decimal). This example would come out to:

6 A E

Sometimes written as 6AExh. Now do the decimal:

0 1 1 0 1 0 1 0 1 1 1 0

2048 1024 512 256 128 64 32 16 8 4 2 1

So, 1024+512+128+32+8+4+2 = 1,710(barring any addition errors that should be it). Most of my students get errors in the decimal portion due to addition errors. Give it a try and its best to do it a few times on paper to practise. Once you get that down, it will be straightforward after that.

If you want some more examples, let me know and I will put some more up.

Hope this helps.