1. Hexadecimal

2. Recap – denary value?
1001

3. 1001 9

4. Recap – denary value?
1111

5. 1111 15

6. Largest number that could be stored in a Byte (8 bits)?

7. Overflow error? What does that mean?
When adding two binary values, if the answer is larger than the maximum value that could be stored then an overflow error occurs.
For example if the values 209 and 128 are added together the answer 337 cannot be stored in a Byte as it is too large. The extra bit (9th) is the overflow error.

9. Hexadecimal Number System
Computers use the binary number system to operate. However, it is possible to make a mistake using long lists of binary numbers.
Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F
The hexadecimal number system is based on 16 states. Digits 0 to 9 are used, followed by letters A to F.

10. Binary, Denary, Hex Table
Hexadecimal
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 10 A
1011 11 B
1100 12 C
1101 13 D
1110 14 E
1111 15 F

11. Representing 182 in the various number systems.
Binary ( )
Denary (182)
Hex (B6)
(B)

12. Convert Denary into Two-Digit Hexadecimal
Convert denary 158 into hexadecimal.
Using the base 16 number system it is clear that 256 is too large for 158.
So the next option is 16. Divide 158/16 = 9 remainder 14.
Remember that the Hex for 14 is E!
So the hex value is 9E (the E is for the 14)
Therefore, denary 158 is equal to 9E hexadecimal.

13. Convert 200 to hexadecimal
Convert denary 200 into hexadecimal.
Convert the denary number to binary using the binary method covered previously.

14. Convert 120 to hexadecimal
Convert denary 120 into hexadecimal.
Convert the denary number to binary using the binary method covered previously.

15. Converting Hex to denary
Convert hexadecimal B6 into denary.
Remember that the first value (B) is multiplied by 16. Also remember that as A is 10, B is 11.
Therefore (11 x 16) + (6 x 1)
So B6 Hexadecimal = 182 Denary

16. Converting Hex to denary
Convert hexadecimal C2 into denary

17. Converting Hex to denary
Convert hexadecimal A4 into denary

18. Past Paper Questions

19. Past Paper Questions

20. Past Paper Questions

21. More conversions
on following slides…

22. 184 to Hex
184 / 16 = x 16 = 8 therefore remainder is 8 11 remainder = B8 in Hex

23. 190 to Hex
190/16 = x 16 = remainder = B, 14 = E 190 = BE in Hex

24. 8D to Binary
8 = 1000 D = 13 = D =

25. B8 to Binary
B = 11 = = 1000 B8 =

26. to Hexadecimal
1111 = 15 = F
0111 = 7 = 7
= F7

27. to Hexadecimal
1011 = 11 = B
0111 = 7 = 7
= B7