1. Candidates should be able to:
Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa
Add two 8-bit binary integers and explain overflow errors which may occur
Convert positive denary whole numbers (0-255) into 2-digit hexadecimal numbers and vice versa.
Convert between binary and Hex equivalents of the same number
Explain the use of Hex numbers to represent binary numbers

2. Starter
Have a go at converting denary to binary numbers on the booklet provided

3. Adding binary numbers together
FEW RULES:

4. Adding Binary
This clip shows you how binary numbers can be added together.

5. Adding binary numbers together

6. Adding binary numbers together
Step 1: Start off by putting the numbers in the top 2 rows in a 4 row table.
3rd row will hold any carry overs
4th row will contain the answer

7. Adding binary numbers together
Step 2: Add the column on the right together From the rules above we know that 1+1 = 10

8. Adding binary numbers together
Step 2: Put a 0 on the bottom row & we carry a 1 over into column 7

9. Adding binary numbers together
Step 3: Column 7 Add the 3 rows together = 10

10. Adding binary numbers together
Step 3: Column 7 Put 0 at bottom of column 7 Carry the 1 to row 3 of column 6

11. Adding binary numbers together
Step 4: Column = 10

12. Adding binary numbers together
Step 4: Column 6 Put 0 down Carry 1 over to column 5

13. Adding binary numbers together
Step 5: Column = 11

14. Adding binary numbers together
Step 5: Column 5 Put 1 down in column 5 Carry 1 over to row 3 column 4

15. Adding binary numbers together
Step 6: Column = 11

16. Adding binary numbers together
Step 6: Column 4 Put 1 down in column 4 Carry 1 over into column 3

17. Adding binary numbers together
Step 7: Column

18. Adding binary numbers together
Step 7: Column 3 Put 1 down in column 3 row 4 Carry 0 to column 2

19. Adding binary numbers together
Step 8: Column =0

20. Adding binary numbers together
Step 8: Column 2 Put 0 down in column 2 row 4 Carry 0 into column 1 row 3

21. Adding binary numbers together
Step 9: Column = 1

22. Adding binary numbers together
Step 9: Column 1 Put 1 down in column 1 row 4 Nothing to carry over

23. Adding binary numbers together
RESULTS:

24. Overflow Errors
The last binary add was straightforward. HOWEVER what would happen if the sum in column 1 had been 1+1?
The carried 1 would have nowhere to go and would be lost.
The problem is called overflow and causes the wrong answer.

25. Overflow Errors
To “solve” this problem what normally happens is a flag in the CPU (processor)
The software that has caused the error MUST check to see if this flag has been set - & if so it has to handle the problem.

26. Hexadecimal Numbers
Hexadecimal is the name given to numbers using base 16
Decimal numbers 10 – 15 are represented using letter A – F
16 values so base 16

27. Hexadecimal
Used in computing as it is a much shorter way of representing a byte of data. Binary data = 8 digits, Hexadecimal data = 2 digits
E.G = FF
Largest byte value is 255 and hexadecimal can represent up to that number

28. Hexadecimal