The document discusses number systems including binary, decimal, and hexadecimal. It provides examples of converting between these number systems. Key points covered include: - Binary uses 0 and 1, decimal uses 0-9, and hexadecimal uses 0-9 and A-F - Conversions can be done between any two number systems by placing the value in the appropriate column based on the system's base (e.g. binary is base 2, decimal is base 10, hexadecimal is base 16) - Examples are provided for converting decimal to binary, binary to decimal, decimal to hexadecimal, hexadecimal to decimal, and between binary and hexadecimal.

1. 1
NUMBER SYSTEM AND
REPRESENTATION
2.2 Number System
2.2.1 Binary
2.2.2 Hexadecimal
2.2.3 Conversion Between Binary and
Hexadecimal
Chapter
PDT - 2017/2018

2. Define Number
System
● A set of numerals for representing
numbers
Decimal Numbers (base 10)
Binary Numbers (base 2)
Hexadecimal Numbers (base 16)
Page 260
Figure 5-2
8
Discovering Computers : Chapter 5

3. Decimal Numbers
● Consists of numbers 0-9
● Decimal digits are joined together to form
longer decimal numbers
● Example: 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11,
12,………
● also known as the base 10 numbering system
8
6 1 5
6 x 10^2 1 x 10^1 5 x 10^0
6 x 100 1 x 10 5 x 1
600 + 10 + 5 = 615

4. At the end of this topic, students
should be able to:
represent data in binary forma)
1
NUMBER SYSTEM AND
REPRESENTATION
2.2.1 Binary
Chapter
PDT - 2017/2018

5. Binary Numbers
● Machine recognises two states: 0 (off) and 1
(on)
● Binary number represents numeric values
using two symbols, 0 and 1
● Eg : 111000, 101 111 111
8

6. Comparison Between Decimal Number
and Binary Number
8
DECIMAL BINARY
0 0
1 1
2 10
3 11
4 100
5 101
6 110
DECIMAL BINARY
7 111
8 1 000
9 1 001
10 1 010
11 1 011
. .
40 101 000
. .

7. At the end of this topic, students
should be able to:
represent data in hexadecimal forma)
1
NUMBER SYSTEM AND
REPRESENTATION
2.2.2 Hexadecimal
Chapter
PDT - 2017/2018

8. Hexadecimal Numbers
● Uses 16 symbols: 0,1,2, 3, 4, 5, 6, 7, 8, 9, A, B,
C, D, E and F.
● It can represent binary values in compact
form.
● 9B416
is example of hexadecimal numbers.
8

9. Comparison Between Decimal Number
and Hexadecimal Number
8
DECIMAL HEXADECIMAL
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
DECIMAL HEXADECIMAL
10 A
11 B
12 C
13 D
14 E
15 F
16 10
17 11
20 14
35 23

10. 8
Decimal Hexadecimal Binary
0 0 0
1 1 1
2 2 10
3 3 11
4 4 100
5 5 101
6 6 110
7 7 111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Comparison Between Number System

11. At the end of this topic, students
should be able to:
a. convert from binary to hexadecimal
b. convert from hexadecimal to binary
1
NUMBER SYSTEM AND
REPRESENTATION
2.2.3 Conversion Between Binary and Hexadecimal
Chapter
PDT - 2017/2018

12. Conversion Between Number System
● Decimal to Binary
● Binary to Decimal
● Decimal to Hexadecimal
● Hexadecimal to Decimal
● Binary to Hexadecimal
● Hexadecimal to Binary
8

13. CONVERSION
Decimal to Binary conversion

14. Binary
number
2
2 ---- 0
---- 1
2
2
---- 1
---- 0
22
11
5
2
1
0 ---- 1
Hence, 22 = 10110 2
Eg 1: Convert the number 22 to the binary
number system. Solution : 22
=
2
2
Write from bottom to
top → left to right
Decimal to binary conversion

15. Eg 2: Convert the number 40 to the
binarynumber system. Solution : 40 =
2
2
2
2
2
2
2
40
20
10
5
2
1
0
---- 0
---- 0
---- 0
---- 1
---- 0
---- 1
Binary
number
Hence, 40 = 101000
2
Write from bottom to
top → left to right
Decimal to binary conversion

16. 2
2
2
2
2
18
9
4
2
1
0
---- 0
---- 1
---- 0
---- 0
---- 1
Binary
number
Hence, 18 = 100102
Eg 3:Express 18 in binary number form
Solution 18 = 2
Write from bottom to
top → left to right
Decimal to binary conversion

17. CONVERSION
Binary to Decimal conversion

18. ● In binary number, the column weights
(again from right to left) are as follows:
● Eg : convert 1011 2 to decimal number
Binary to Decimal conversion
1 0 1 1
1 x (2^3) 0 x (2^2) 1 x (2^1) 1 x (2^0)
1 x 8 0 x 4 1 x 2 1 x 1 Decimal number
8 0 2 1
8+0+2+1=1110
Binary to decimal conversion
CONVERSION
Eg 1: Convert the number 10112 to the
decimal

19. Hence, 10110 2 = 22
Eg 1: Convert the binary number 10110 2 to
decimal number
Solution:
1 0 1 1 0
1 x 2^4 0 x 2^3 1 x 2^2 1 x 2^1 0 x 2^0
2210
1 x 16 0 x 8 1 x 4 1 x 2 0 x 1
16 0 4 2 0
16 + 0 + 4 + 2 + 0 =
Binary to decimal conversion
CONVERSION
Eg 2: Convert the number 101102 to the
decimal

20. Eg 2 :Convert the binary number 1011100 2
to decimal number
Solution:
Hence, 1 011 100 2 = 92
1 0 1 1 1 0 0
1 x 2^6 0 x 2^5 1 x 2^4 1 x 2^3 1 x 2^2 0 x 2^1 0 x 2^0
9210
1 0 1 1 1 0 0
1 x 64 0 x 32 1 x 16 1 x 8 1 x 4 0 x 2 0 x 1
64 + 0 + 16 + 8 + 4 + 0 + 0
=
Binary to decimal conversion
CONVERSION
Eg 3: Convert the number 10111002 to the
decimal

21. CONVERSION
Decimal to Hexadecimal
conversion

22. 16
16
16
1341
83
5
0
---- 3
---- 5
Eg 1: Convert the decimal number 1341 to
hexadecimal number
Hence,1341 = 53D16
Decimal to hex conversion
Hex Number
Write from bottom to
top → left to right
---- 13 = D

23. Eg 2 : Convert the decimal number 860 to
hexadecimal number
16
16
16
860
53
3
0
---- 12 = C
---- 5
---- 3
Hence, 860 = 35C16
Hex Number
Decimal to hex conversion
Write from bottom to
top → left to right

24. 16
16
16
2020
126
7
0
---- 4
---- 14 = E
---- 7
Eg 3 : Convert the decimal number 2020 to
hexadecimal number
Hex Number
Decimal to hex conversion
Hence, 2020 = 7E416
Write from bottom to
top → left to right

25. CONVERSION
Hexadecimal to Decimal
conversion

26. to decimal number● Convert
AFB216
Solution:
Hence, AFB216 =
44978
Eg 1 : Convert the hex number, AFB216
to decimal number
A F B 2
A x 16^3 F x 16^2 B x 16^1 2 x 16^0
4497810
10 x 4096 15 x 256 11 x 16 2 x 1
40960 + 3840 + 176 + 2 =
hex to decimal conversion
CONVERSION
Eg 1: Convert the number AFB16 to the
decimal

27. to decimal number● Convert
BA816
Solution:
Hence, BA816 =
2984
Eg 2 : Convert the hex number, BA816
to decimal number
B A 8
B x 6^2 A x 16^1 8 x16^0
298410
11 x 256 10 x 16 8 x 1
2816 + 160 + 8 =
hex to decimal conversion
CONVERSION
Eg 2: Convert the number BA816 to the
decimal

28. to decimal number● Convert AFFA16
Solution:
Hence, AFFA16 =
45050
Eg 3 : Convert the hex number, AFFA16
to decimal number
A F F A
A x 16^3 F x 16^2 F x 16^1 A x16^0
4505010
10 x 4096 15 x 256 15 x16 10 x
1
40960 + 3840 + 240 + 10 =
hex to decimal conversion
CONVERSION
Eg 3: Convert the number AFFA16 to the
decimal

29. CONVERSION
Binary to Hexadecimal
conversion

30. Binary to Hexadecimal conversion
● There are two ways on how to convert
the
binary to hexadecimal number.
● 1st way : Decimal
Hexadecimal
○ Binary
○ 2nd way :
○ Binary Hexadecimal
binary to hex conversion

31. Eg. 1: Convert the binary number 110102 to
hexadecimal 1st way
○ Binary Decimal
26
1
16
16
0
---- 10 = A
---- 1
Decimal Hexadecimal
Hence, 11010 2 = 1A16
1 1 0 1 0
1 x 2^4 1 x 2^3 0 x 2^2 1 x 2^1 0 x 2^0
26
1 x16 1 x8 0 x 4 1 x 2 0 x 1
16 + 8 + 0 + 2 + 0 =
Eg. 1: Convert the binary number 110102 to
hexadecimal 1st way

32. ● Step 1: divide the given binary digit into 4 digit per
group from right to left.
1 1 0 1 0
● Step 2: Using 8421 table,
1 1 0 1 0
1
= 1
8 4
2
1
8 + 2
= 10
= A
8 4 2 1
Hence, 11010 2 =
1A16
Eg. 1: Convert the binary number 110102 to
hexadecimal 2nd way

33. Binary Decimal
binary to hex conversion
18
1
0
---- 2
---- 1
Decimal
16
16
Hexadecimal
Hence, 100102 = 1216
Hex number
Eg.2 :Convert the binary number 100102 to
hexadecimal 1st way
1 0 0 1 0
1 x 2^4 0 x 2^3 0 x 2^2 1 x 2^1 0 x 2^0
18
1 x 16 0 x 8 0 x 4 0 x 2 0 x 1
16 + 0 + 0 + 2 + 0 =
Eg. 2: Convert the binary number 100102 to
hexadecimal 1st way

34. Eg.2 :Convert the binary number 100102 to
hexadecimal 2nd way
● Step 1: divide the given binary digit into 4 digit per
group from right to left.
1 0 0 1 0
● Step 2: Using 8421 table,
1 0 0 1 0
1
= 1
8 4
2
1
2
= 2
8 4 2 1
Hence, 11010 2 =
1216

35. CONVERSION
Hexadecimal to Binary
conversion

36. Hexadecimal to Binary conversion
● There are two ways on how to convert
the
hexadecimal to binary number.
● 1st way : Decimal
Binary
○ Hexadecimal
○ 2nd way :
○ Hexadecimal Binary
binary to hex conversion

37. Eg 1: Convert the hexadecimal number
3FD to binary number 1st way
Hexadecimal Decimal
16^2 16^1 16^0
1021
3 F D
256 x3 16 x15 1 x 13
768 + 240 + 13 =
hex to binary conversion
Eg. 1: Convert the hexadecimal number
3FD16 to binary number 1st way
Hexadecimal Decimal

38. Binary number
De
2
2
2
2
1021
510 ---- 1
255 ---- 0
127 ---- 1
2 63 ---- 1
2 31 ---- 1
2 15 ---- 1
2 7 ---- 1
2 3 ---- 1
2 1 ---- 1 Hence, 3FD16 = 11111111012
0 ---- 1
cimal Binary
hex to binary conversion
Eg. 1: Convert the hexadecimal number
3FD16 to binary number 1st way

39. Eg 1: Convert the hexadecimal number
3FD to binary number 2nd way
Hence, 3FD16 = 11111111012
=8+4+1
= 13
=8+4+2+1
= 15
=2+1
= 3
3 F = 15 D = 13
3 15 13
8 4 2 1 8 4 2 1 8 4 2 1
0 0 1 1 1 1 1 1 1 1 0 1
Eg. 1: Convert the hexadecimal number
3FD16 to binary number 2nd way
hex to binary conversion

40. Eg 2: Convert the hexadecimal number 1A2
to binary number 1st way
hex to binary conversion
Hexadecimal Decimal Decimal Binary
2
2
2
2
2
2
2
2
2
2
---- 0
---- 1
---- 0
---- 0
---- 0
---- 1
---- 0
---- 1
---- 1
Hence, 1A216 = 1101000102
1 A 2
1 x 16^2 A x 16^1 2 x 16^0
418
1 x 256 10 x 16 2 x 1
256 + 160 + 2 =
418
209
104
52
26
13
6
3
1
0
Eg. 2: Convert the hexadecimal number
1A216 to binary number 1st way
DecimalHexadecimal Decimal Binary
hex to binary conversion

41. Eg 2: Convert the hexadecimal number
1A2 to binary number 2nd way
=2=8+2
= 10
=1
Hence, 1A216 = 1101000102
1 A 2
1 10 2
8 4 2 1 8 4 2 1 8 4 2 1
0 0 0 1 1 0 1 0 0 0 1 0
= 2= 8 + 2
= 10
= 1
Eg. 2: Convert the hexadecimal number
1A216 to binary number 2nd way
hex to binary conversion

42. UPS 2015/2016
Q: Given the Internet Protocol address of a
printer as 192.0.0.2. Convert the address to
hexadecimal number [2 marks]
A: C0.0.0.2