1. Data Representation – Numbers

2. Basic Binary
1 = switch closed / electricity on, 0 = switch open / electricity off If you send 1 bit, how many different combinations can you send? 1 or 0 If you send 2 bits, how many different combinations can you sent? bits? etc 4 bits? etc. 5 bits? etc.

3. Terminology KB Kilobyte 1000/1024 bytes MB Megabyte 1000/1024 KB GB
Gigabyte
1000/1024 MB TB
Terabyte
1000/1024 GB
Bit
1 or 0
Nibble
4 bits
Byte
2 nibbles / 8 bits

4. Binary - Decimal
128 64 32 16 8 4 2 1 8 1
= 9
128 64 32 16 8 4 2 1
128 32 4 2
= 166

5. Have a go 1 2 3
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
Answers: 1 = 49, 2 = 154, 3 = 247, 4 = 158, 5 = 249, 6 = 741, 7 = 1543, 8 = 2405, 9 = 62423, 10 = 34582

6. Patterns
If the least significant bit (right most) is a 1, the number is odd
All 1s = the next number -1
e.g.
= 127 (is 128-1)
The smallest number in positive binary is always 0
The number of combinations is equal to the next number
= 128 different combinations
0 to 127
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1

7. Decimal - Binary 23
23 – 16 = 7
7 – 4 = 3
128 64 32 16 8 4 2 1 98
98 – 64 = 34
34 – 32 = 2
128 64 32 16 8 4 2 1
242
242 – 128 = 114
114 – 64 = 50
50 – 32 = 18
18 – 16 = 2
128 64 32 16 8 4 2 1

8. Have a go 28 43 78
101
200
Answers: 1 = 11100, 2 = , 3 = , 4 = , 5 = ,
6 = , 7 = , 8 = , 9 = , 10 =

9. Hexadecimal Easier to remember than binary
Quicker/easier to write than binary
Can be converted quickly to binary (and back)
Each nibble is converted into a single hexadecimal number
1 nibble can be:
Decimal Hexadecimal
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F

10. Hexadecimal - binary F20 F 2 0 1111 0010 0000 111100100000
3A 3 A
F20
F 2 0

11. Have a go, hex-bin 11 2A BB 6C 50F A0 9BD D5AA 1974 26ABEB
Answers: 1 = , 2 = , 3 = , 4 = , 5 = , 6 = ,
7 = , 8 = , 9 = , 10 =

12. Binary - Hexadecimal 111101011011 1111 0101 1011 15 5 11 F5B
F5B

13. Have a go, binary-hex
Answers: 1 = 6A, 2 = BF, 3 = 80, 4 = 5F, 5 = E6B, 6 = 2AC, 7 = F0F, 8 = 33F, 9 = 5E2B, 10 = FF16

14. Hexadecimal - Decimal
Convert to binary and then to decimal…
Or…
161
160 3 A
3A =
162
161
160
(3 * 16) + (10 * 1) = 58
162
161
160 1 D 3
1D3 =
256 16 1
(1 * 16 * 16 ) + (13 * 16) + (3 * 1) = 467

15. Have a go, hex-dec 11 50F 2A 9BD BB D5AA 6C 1974 A0 26ABEB
Answers: 1 = 17, 2 = 42, 3 = 187, 4 = 108, 5 = 160, 6 = 1295, 7 = 2493, 8 = 54698, 9 = 6516, 10 =

16. Decimal – Hexadecimal 78 = 4E 199 = C7 299 = 12B 256 16 1 256 16 1 162
Convert to binary and then hexa Or 78
= 4E
199
= C7
299
= 12B
256 16 1 4 14
256 16 1 12 7
162
161
160
256 16 1 2 11

17. Have a go – dec-hex 22 59
100
189
231
257
1056
2000
3578
32444
Answers: 1 = 16, 2 = 3B, 3 = 64, 4 = BD, 5 = E7, 6 = 101, 7 = 420, 8 = 7D0, 9 = DFA, 10 = 7EBC

18. Binary Addition What is 1 + 1? What is 1 + 1 + 1? What is 0 + 1? 1 1
What is 1 + 1? 1
What is 0 + 1? 1
What is ? 1

19. Binary addition – 4 basic rules
0 + 0 = = = 0 carry = 1 carry 1 Delete all boxes for example 1
delete 1

20. 1
Overflow = the result of the addition is too large to fit in 8 bits. A 9th bit is needed to store the result. 1
(1)

21. Have a go, binary addition1 1
Delete boxes for answers 1 1
(1)
(1)
If adding 4 1s, the result is binary , put a 0 in the box carry the 1 across two columns to the left 1 1
(1)
(1)

22. Binary Shifts
Move binary numbers a set number of places to the left, or the right
Logical shift – spaces are filled in with 0s
Arithmetic shift – when shifting left the spaces are filled with 0s, when shifting right they are filled with the MSB

23. Logical 1
Left shift 2 spaces 1 1
Right shift 2 spaces 1

24. Arithmetic 1
Left shift 2 spaces 1 1
Right shift 2 spaces 1

25. What do they do?
Each left shift (log/ari) multiplies the number by 2 (so 3 shifts multiply by 2 x 2 x 2) etc.
Each logical right shift divides the number by 2 (so 2 shifts divides by 4) etc.

26. Have a go, shifts Type Left/Right Num Places Binary 1 Logical Left 2
Arithmetic 3
Right 4 5 6 7 8 9 10
Answers