Lesson Objectives Understand the hexadecimal numbering system Convert numbers between hexadecimal and denary, and vice versa ALL students be able to count in hex from 1 to 16 MOST students will convert hex numbers into denary SOME students will convert numbers between hex, denary and binary

1 2 3 4 1 You already know about base 10 (Decimal/Denary) And you’ve just learnt about base 2 (Binary) 1 2 3 4 10 1000 100 x10 1 2 8 4 x2

Why do we need binary numbers? Because computers work on the principle of 2 states, that something is either ON/TRUE or OFF/FALSE. This can only be done with base 2 (binary) If it was done with decimal/base 10 there would be 10 different states!

The problem with binary… There is one big problem with binary…numbers can become VERY long! In order to make it easier for a human programmers to work with binary numbers, they use the hexadecimal system (like a binary shortcut)

Hexadecimal As we move left, the column headings increase by a factor of sixteen x16 x16 x16 1 2 3 16 4096 256 This number is: 1 x 256 + 2 x 16 + 3 x 1 = 291 It’s still two hundred and ninety-one, it’s just written down differently How can there be sixteen possible digits in each column, when there are only ten digits? http://www.advanced-ict.info/interactive/hexadecimal.html

Hexadecimal Hexadecimal uses the digits 0-9 and the letters A-F to represent the denary numbers 0-15 Den Hex 8 1 9 2 10 A 3 11 B 4 12 C 5 13 D 6 14 E 7 15 F Notice how 0 is classed as a digit, so there are 16 numbers in total from 0 to 15

Making bigger numbers You do it in exactly the same way 16 1 Den 1x16 1x16 1x16 + 1x1 17 A 1x16 + 1xA(10) 26 A(10)x16 160 2 B 2x16 + 1xB(11) 43

Where is it used? When have you seen numbers being represented as letters? Hex is often used for 32-bit colour values, especially on web pages FF00EE99 instead of 11111111000000001110111010011001. http://www.advanced-ict.info/interactive/colours.html

255 Denary 255 Binary 11111111 Hexadecimal FF

Large binary numbers are hard to remember Programmers use hexadecimal values because: each digit represents exactly 4 binary digits; hexadecimal is a useful shorthand for binary numbers; hexadecimal still uses a multiple of 2, making conversion easier whilst being easy to understand; converting between denary and binary is relatively complex; hexadecimal is much easier to remember and recognise than binary; this saves effort and reduces the chances of making a mistake.

You convert denary to hex in the same was as binary 16 1 D 2 Convert the denary number 45 into a hex number Step 1: How many times does 16 go into 45? 45 / 16 = 2 (with 13 remaining) Step 2: How many times does 13 go into 1? 13! 13 in hex is D

Let’s do another one 16 1 7 C Convert the denary number 199 into a hex number Step 1: How many times does 16 go into 199? 199 / 16 = 12 (with 7 remaining) Step 2: 12 in hex is C Step 2: How many times does 7 go into 1? 7! 7 in hex is 7!

Lesson task: Complete the denary to hex conversions in your workbook. Extension: If you complete, have a go at the cross word task in your booklet.

Hex to binary To convert from hexadecimal to binary treat each digit separately. It may be easier to go via denary to get a binary number. So DB in hexadecimal is 11011011 in binary. Hex D B Denary 13 11 Binary 1