Hexadecimal
Table of Contents
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.
Binary | Hexadecimal | Decimal |
---|---|---|
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
and13
- Now convert to Hex -
5
andD
- 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
andE
- Convert each to denary
9
and14
- Then convert each to binary
1*8 + 0*4 + 0*2 + 1*1
and1*8 + 1*4 + 1*2 + 0*1
- Which makes
1001
and1110
- 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