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
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You already know about base 10 (Decimal/Denary)
And you’ve just learnt about base 2 (Binary)
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!
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)
As we move left, the column headings increase by a factor of sixteen
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?
Notice how 0 is classed as a digit, so there are 16 numbers in total from 0 to 15
Hexadecimal uses the digits 0-9 and the letters A-F to represent the denary numbers 0-15
You do it in exactly the same way
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.
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.
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
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!
Complete the denary to hex conversions in your workbook.
Extension: If you complete, have a go at the cross word task in your booklet.
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 to binary