1. Binary and Logic
Computers use electrical signals that are on or off, so they have to see everything as a series of binary numbers. This data is represented as a sequence of 1s and 0s (on or off). All data that we want a computer to process needs to be converted in to this binary format.
Watch Video – What are binary numbers.

2. Binary Basics Binary is a number system with base 2.
Only 2 digits (0 and 1) are used to write every number.
This is the foundation of almost every computer program.

3. Binary Basics Binary to denary (base 10)
Each number in binary represents a power of 2, the same way each number in base 10 represents a power of 10. For instance – take the number 1357
This gives us – (1*1000) + (3*100) + (5*10) + (7*1) = 1357
1000s
100s
10s 1s 1 3 5 7

4. Binary Basics Binary to denary (base 10)
The same applies for binary (base 2) but with powers of 2
For instance – take the number
Looking only at where the ones are – this gives us:
(1*128)+(1*16)+(1*4)+(1*1) or
= 149
128 64 32 16 8 4 2 1

5. Binary Basics Binary to denary (base 10)
Each binary digit above is called a bit.
There are 8 bits in the example above.
8 Bits are also called a byte.
4 Bits are called a nibble.
Two nibbles make a byte.
128 64 32 16 8 4 2 1

6. Binary Basics
Task 1
Complete Binary worksheet 1

7. Binary Basics
Task 2
Write out 10 of your own binary numbers to solve. Use any where from a nibble to a byte.
Give these to someone else to convert then check to see if they have got the right answers.

8. Binary Basics Denary to Binary
There are many ways of doing this. Here we will show you a couple of methods
Method 1
Take the number and divide it by 2 and show the remainder. For instance – 130
Sum
Result
Remainder
130 / 2 65

9. Binary Basics Denary to Binary Then you keep going…. Sum Result
Remainder
130 / 2 65
65 / 2 32 1
32 / 2 16
16 / 2 8
8 / 2 4
4 / 2 2
2 / 2

10. Binary Basics 10000010 Denary to Binary
You should always be left with 1. Starting with that read back up the remainder column to give you your answer.
Sum
Result
Remainder
130 / 2 65
65 / 2 32 1
32 / 2 16
16 / 2 8
8 / 2 4
4 / 2 2
2 / 2

11. Binary Basics 10000010 Denary to Binary Lets test to see if it works=
= 130
So this method works fine.
128 64 32 16 8 4 2 1

12. Binary Basics
Task 3
Using Method 1 Convert the following numbers into binary. 75
127 56
100 24

13. Binary Basics Denary to Binary Method 2
Here we just keep subtracting the powers of 2 until we have nothing left. For instance let us look at the number 196
196 – 128 = 68 so we can put a 1 in the 128 position
128 64 32 16 8 4 2 1

14. Binary Basics Denary to Binary Method 2 .. continued
68 – 64 = 4 so we can put a 1 in the 64 position
4-32 = -28 – so 0 in the 32 position
And so on. Here we can see we only have 4 left so we can put 1 in the four position and leave everything else as 0 giving us –
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1

15. Binary Basics Denary to Binary Method 2 .. continued
To confirm that then..
= 196
128 64 32 16 8 4 2 1

16. Binary Basics
Task 4
Using Method 2 Convert the following numbers into binary using 8 bits (byte)
204
177 25
244 89

17. Binary Basics
Task 5
Have a go at Binary Worksheet 2

18. Binary Basics Task 6 Have a go of the following game.

19. Binary Basics
Task 7
Have a look at the following page and try out the questions

20. Binary Basics Task 8 Have a go at the following game.