1. Conversions Denary to Binary Method 1
Divide the number repeatedly by two and note the carry. For example
178 to binary
178 / 2 = 89 reminder 0
89 / 2 = 44 remainder 1
44/2 = 22 remainder 0
22/2 = 11 remainder 0
11/2 = 5 remainder 1
5/2 = 2 remainder 1
2/2 = 1 remainder 0
1 = 1
So starting from the bottom 178 is in binary

2. Conversions Denary to Binary Method 2
Set out the binary positions and if the number – that position is a positive – put a 1 in it.
For example
178 – 128 = 50 – so 1 in the 128 position
50 – 64 = -14 so a 0 in the 64 position
50 – 32 = 18 so 1 in the 32 position
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1

3. Conversions Denary to Binary Method 2
18-16 = 2 so 1 in the 16 position
2-8 = -6 so 0 in the 8 position
2-4 = -2 so 0 in the 4 position
2-2 = 0 so 1 in the 2 position
Leaving 0 in the 1 position
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1

4. Conversions Binary to Denary Method 1
Work out the position values of the binary bits and add those values together
So above would be
= 178
128 64 32 16 8 4 2 1

5. Conversions Denary to hexidecimal Method 1
Divide the number repeatedly by 16 until you have a number less than 16. For example:
178 / 16 = 11 remainder 2 So
2 becomes B2
1076 / 16 = 67 remainder 4
67 / 16 = 4 remainder 3
4 = 4
So 1076 is 434 in hexadecimal.

6. Conversions Denary to hexidecimal Method 2
Each number of a hexadecimal converts to 4 bits so you could work out the denary number in binary first then split it into 4 bits and work out the hex numbers from that.
1076 =
Now split into 4s
And work out the value of each 4 bits separately.
0100 = 4
0011 = 3
2048
1024
512
256
128 64 32 16 8 4 2 1 8 4 2 1

7. Conversions Hexidecimal to Denary Method 1
Each unit of a Hex number is going to be a power of 16 so you just multiple each number by that power and add them together.
So AF9 is
So this will be
(10 * 256) + (15*16) + (9*1) =
= 2809
256 16 1 A F 9

8. Conversions Hexidecimal to Denary Method 2
Convert the number to binary by just taking each unit as four bits and then do a binary to denary conversion
So AF9 is
Then convert that back to denary =
= 2809 8 4 2 1 A F 9
2048
1024
512
256
128 64 32 16 8 4 2 1

9. Conversions Binary to Hexidecimal and back again Method 1
Split the Binary number into 4 bits each and each four bits then represents a single hexadecimal number, for example:
To convert from Hex back to binary you just reverse the procedure. 8 4 2 1 E D 3