Hexadecimal

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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 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