You've already learned about Binary (base2) numbers, and why Computers use them. Now let's look at another base - base16, called Hexadecimal

## 1 Why not binary?

### Learn It

• Binary numbers are difficult for programmers to work with.
• If we're building a web-page, then chances are we're going to want to use colour.
• In general computers use the RGB colour model, where any colour we need is made up by additive mixing Red, Green and Blue.
• The value of RGB colours ranges from 0,0,0 up to 255,255,255.

Here's a colour that is represented as R-159, G-028, B-173.

### Try It

• Convert each of the 3 digit denary numbers to binary, as see what you get.
• Do you think that writing the binary number for the colour would be convenient.

### Document It

• Note down why it is that programmers don't like using binary in their code.

## 2 Hexadecimal is easier

### Learn It

• Coders use Hexadecimal as it's easy to convert it to binary, but it is more succinct.
• When counting in Hexadecimal, we use the letters A-F after reaching 9.
• `0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F`
• Normally we would use a table to aid in the conversion.
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 A 10
1011 B 11
1100 C 12
1101 D 13
1110 E 14
1111 F 15
• We can take a binary number, such as 10101101.
• Split it up into nibbles - 1010 1101
• Convert each to Hex - AD

### Try It

• Convert each of the binary numbers you worked out before, into their hex equivalents.
• Now go on line and look up the hex code you've calculated (place a # in front of the number in your search) and check it matches the colour on this web-page.

### Learn It

• With experience, you'll not need a table, as you'll come to recognise the hex equivalent for each nibble.
• However, if you don't have a conversion table or can't remember the values, you can convert between binary and hex, by using denary as a middle step.
• Lets start with the binary number `01011101`
• Split it into nibbles - `0101 1101`
• Convert to denary - `1*1 + 0*2 + 1*4 + 0*8` and = `1*1 + 0*2 + 1*4 + 1*8`
• So we get - `5` and `13`
• Now convert to Hex - `5` and `D`
• So the Hex is 5D

### Try It

• Convert the following binary numbers to hex and show your working. Check them by using the table.
• 11110011
• 00101100
• 10101010

### Document It

• Make notes on binary to hex conversion, detailing how it is done.

### Research It

• Go online and look up hex codes for colours.
• Make notes on how hex codes are used to represent colours in computers.

## 3 Hex to binary conversion

### Learn It

• Converting hex to binary is a fairly similar process. We just need to do the denary conversion in between.
• Take the number `9E`
• Split it up `9` and `E`
• Convert each to denary `9` and `14`
• Then convert each to binary `1*8 + 0*4 + 0*2 + 1*1` and `1*8 + 1*4 + 1*2 + 0*1`
• Which makes `1001` and `1110`
• Which together becomes `10011110`

### Try It

• Convert the following Hex values to binary and show your working. Use the table to check your answers.
• 3F3F3F
• 88833A
• ABCDEF