1. Binary Arithmetic

2. Learning Objectives
3.1.4 Be able to perform binary arithmetic [add, subtract, multiply] and understand the concept of overflow

3. Addition…
= 62… why?
Remember that the position of the number is related to it’s value, so a carry in denary is worth 10 units.
It’s the same in binary – remember the position relates to it’s value!
10’s
1’s 2 6 3
2+3+1 = 6
6+6 = 1 ten 2 units
Carry 1 ten

4. Binary Addition Lets’ try 101 + 101 = 8’s 4’s 2’s 1’s 1
2+0+0 = 1 lot of 2
Carry 1 lot of 8
4+4 = 8
Carry 1 lot of 2
1+1 = 2

5. Some more examples - Try the following – 0101+0100 = 0111+0001 == =
This might cause a problem… =
1001
1000
0111
1100
10000

6. Overflow! That’s what happens when “you run out of bits”
If you try to store a number that is larger than the number of bits you have, you create an Overflow error.
These are bad!
Normally the result is treated as a negative!

7. Binary subtraction. Computers can only ADD… …well that’s a problem.
What about … = 2?
We can work with that!

8. Subtraction…in binary
Lets try 0101 – 0011
5 – 3
We know the answer should be 2.
We need the Two’s compliment for -3.
Flip all the bits 1100
Add 1 to answer 1101
8’s
4’s
2’s
1’s 1
IGNORE ANY CARRY!

9. Some more examples… Try these – 8 - 7 = 12 – 4 = 5 – 5 = 7 – 3 =
7 – 3 =
6 – 2 =

10. And finally – Multiplication.
How have you been taught to multiply numbers together?
For example 5 * 11 = 55?
How did you work it out?
Show method on board
Now try 18 * 36 = …
648

11. What ever your method…try this

12. Remember why you move over!
Remember when you move over a column in DENARY it’s because the number is 10 times greater!
When we do the same in binary it’s because it is TWICE as large!

13. https://youtu.be/ZS4Ql5vQbRY
Watch this example…
Be ready to talk about it afterwards!

14. 3 x 5 = 15. 16 8 4 2 1 1 1 1 1 1 1 1 1
Start using the method we have seen. From the right.
Remember we are multiplying 2 x 1 when we move columns. So the answer has to be stored in the 2 column!
Add up everything.
We move over to the 2’s.
0 x anything is always 0.
We have now finished with the least significant bit of 5. the 1’s.
We have now finished with the 2’s. We move to the 4’s
4 x 1 = 4
4 x 2 = 8

15. Examples.. Now try these… 2 x 4 = 0010 * 0100 = 3 x 8 = 0011 * 1000 =

16. Plenary HOW do you add 2 binary numbers together? What is overflow?
Can you get overflow when subtracting?
HOW do you subtract one binary number from another?
HOW do you multiply 2 numbers together?