1. 2.0 COMPUTER SYSTEM 2.2 Number System and Representation

2. Learning Outcome At the end of this topic, students should be able to:
2.2.1 Binary
Represent data in binary form
2.2.2 Hexadecimal
Represent data in hexadecimal form
2.2.3 Conversion between binary and hexadecimal
Convert from binary to hexadecimal
Convert from hexadecimal to binary

3. Numbering System Introduction Concept
A numbering system is a way of representing numbers.
Common numbering system used is called the decimal numbering system / base 10 numbering system
The decimal numbering system is the numbering system that represents all numbers using 10 symbols (0 – 9).
Exp: 2310

4. Binary Numbering System
2.2.1
Concept
The numbering system that has just two unique digits, 0 and 1, called bits.
Exp: 10102 1 2 3 4 5 6 7 8 9
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001

5. Binary Numbering System
2.2.1
Why?
Computer uses the binary numbering system to represent the electronic status of the bits in memory. It also is used for other purposes such as addressing the memory locations.

6. Hexadecimal Numbering System
2.2.2
Concept
The numbering system that uses 16 different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F).
Exp: 53D16

7. Hexadecimal Numbering System
2.2.2
Why?
Hexadecimal notation is a shorthand method for representing the binary digits stored in a computer.
e.g.:
– can easily be misread by people,
hexadecimal notation groups binary digits into units of four, which in turn are represented by other symbols; i.e. C9A116

8. Hexadecimal Symbol
Decimal Equivalent
Binary Equivalent
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8
1000 9
1001 A 10
1010 B 11
1011 C 12
1100 D 13
1101 E 14
1110 F 15
1111

9. Conversion Between Binary and Hexadecimal
2.2.3
1. Decimal to Binary
2. Binary to Decimal
3. Decimal to Hexadecimal
4. Hexadecimal to Decimal
5. Binary to Hexadecimal
6. Hexadecimal to Binary

10. 1. Decimal to Binary - (base 10 to base 2)
Division – Remainder Method
(Divide by 2, find the remainder)
(2) Convert to binary 2
156 78 39 19 1 9 4
(1) Convert 2310 to binary 2 23 11 1 5
Ans :
*Read the remainder from below
Ans :

11. 1. Decimal to Binary - (base 10 to base 2)
Division – Remainder Method
(Divide by 2, find the remainder)
Try this: Convert 5610 to binary

12. 2. Binary to Decimal - (base 2 to base 10)
Place Value Method
e.g. Convert to decimal
Step 1 1
Step 2 16
(24 ) 8
(23 ) 4
(22) 2
(21)
(20)
Step 3
8 +
4 +
0 + X X X X X
Place value
= 2910 12

13. 2. Binary to Decimal - (base 2 to base 10)
Place Value Method
Try this: Convert to decimal
Step 1
Step 2
Step 3 13

14. 3. Decimal to Hexadecimal - (base 10 to base 16)
Division – Remainder Method
(Divide by 16, find the remainder)
e.g. Convert 7710 to hex 16 77 4 13
= D
Read the remainder as hex number
= 4D16 14

15. 3. Decimal to Hexadecimal - (base 10 to base 16)
Division – Remainder Method
(Divide by 16, find the remainder)
Try this: Convert 9110 to hex 15

16. 4. Hexadecimal to Decimal - (base 16 to base 10)
Place Value Method
e.g. Convert 4D16 to decimal
Step 1 4 D
Step 2 13
Step 3 16
(161) 1
(160)
Step 4
64 +
Decimal equivalent X X
Place value
= 7710 16

17. 4. Hexadecimal to Decimal - (base 16 to base 10)
Place Value Method
Try this: Convert AF1016 to decimal
Step 1
Step 2
Step 3
Step 4 17

18. 5. Binary to Hexadecimal - (base 2 to base 16)
Step 1: Convert Binary to Decimal
Place value method
Step 2: Convert Decimal to Hex
Division – Remainder Method
(Divide by 16, find the remainder) 18

19. 5. Binary to Hexadecimal - (base 2 to base 16)
Step 1: Place Value Method e.g. Convert to decimal
Step 1 1
Step 2 16
(24 ) 8
(23 ) 4
(22) 2
(21)
(20)
Step 3
0 +
4 + X X X X X
Place Value
= 2110 19

20. 5. Binary to Hexadecimal - (base 2 to base 16)
Step 2: Division – Remainder Method (Divide by 16, find the remainder) e.g. Convert 2110 to hex 16 21 1 5
Read the remainder as hex number
= 1516 20

21. 5. Binary to Hexadecimal - (base 2 to base 16)
Try this: Convert to hex 1. Step 1 ? 2. Step 2 ? 21

22. 5. Binary to Hexadecimal - (simplify method)
4 Bits = 1 Hex digit
e.g. Convert to hex
Group to 4 bits
(R to L)
Step 1
0010
1011
1101
Step 2
8421
Step 3 2 11 13
Step 4 B D
Place value
Decimal equivalent
Hex equivalent
= 2BD16 22

23. 6. Hexadecimal to Binary - (base 16 to base 2)
Step 1: Convert Hexadecimal to Decimal
Place Value Method
Step 2: Convert Decimal to Binary
Division – Remainder Method
(Divide by 2, find the remainder) 23

24. 6. Hexadecimal to Binary - (base 16 to base 2)
Step 1: Place Value Method e.g. Convert F116 to decimal
Step 1 F 1
Step 2 15
Step 3 16
(161)
(160)
Step 4
Decimal equivalent X X
Place Value
= 24110 24

25. 6. Hexadecimal to Binary - (base 16 to base 2)
Step 2: Division – Remainder Method (Divide by 2, find the remainder) e.g. Convert to binary 2
241
120 1 60 30 15 7 3
*Read the remainder from below = 25

26. 6. Hexadecimal to Binary - (base 16 to base 2)
Try this: Convert 1E16 to binary 1. Step 1 ? 2. Step 2 ? 26

27. 6. Hexadecimal to Binary - (simplify method)
1 Hex digit = 4 Bits
e.g. Convert 9AF16 to binary
Break up each digit
Step 1 9 A F
Step 2 10 15
Step 3
8421
Step 4
1001
1010
1111
Decimal equivalent
Place value
Group all digits = 27

28. TO BASE FROM BASE 2 10 (Decimal) 16 (Hexadecimal) Place Value Method
(Binary) 10
(Decimal) 16
(Hexadecimal)
Place Value Method
Simplify Method
(4 Bits = 1 Hex digit) - 28

29. TO BASE FROM BASE 2 (Binary) 10 (Decimal) 16 (Hexa decimal)
Simplify Method
(1 Hex digit = 4 Bits)
Place Value Method - 29

30. TO BASE FROM BASE 2 (Binary) 10 (Decimal) 16 (Hexadecimal) –
Division – Remainder Method
(Divide by 2, find the remainder) –
(Divide by 16, find the remainder) - 30

31. TRY This…
Convert hexadecimal AF116 to binary number.

32. TRY This…
Express 4010 in binary number.

33. TRY This…
Convert the decimal number to hexadecimal number.

34. TRY This…
Convert to hexadecimal number.