This document discusses different number systems including decimal, binary, octal, and hexadecimal. It provides details on how each system uses a different base and symbols. The key points covered include: - Decimal uses base 10 with digits 0-9. Binary uses base 2 with digits 0-1. Octal uses base 8 with digits 0-7. Hexadecimal uses base 16 with digits 0-9 and A-F representing 10-15. - Methods are described for converting between the different number systems including using powers of the base and shortcut tables for binary, octal, and hexadecimal. - Examples are provided of converting decimal numbers to and from the other number systems through successive division and using place values of the base.

1. NUMBER SYSTEM
SHILPA KRISHNA
RESEARCH SCHOLAR

2. NUMBER SYSTEM
DECIMAL BINARY OCTAL HEXADECIMAL

3. DECIMALNUMBER SYSTEM
• The number system that we use in our day-to-life
• In this number the base is 10.ie,total number of digits or
symbols is ten.
• Example:
The value of the decimal number 4137 is calculated as -
4*1000 + 1*100 + 3*10 + 7*1
7000 100 30 7
Thousands Hundreds Tens Units
Position position position position

4. BINARY NUMBER SYSTEM
• Number system has two symbols 0(zero) and 1(one) called
Binary Digits or bits. Its base is 2.
• The weights assigned to bits in this system are powers of 2,
namely 20 , 21 , 22 ……
1 0 1 0 1
Most Significant Bit Least Significant Bit

5. OCTALNUMBER SYSTEM
• In this system there are only 8 digits ie.
0,1,2,3,4,5,6,7
• Its base is 8. Each position in an octal
number represents a power of 8
ie, 80 , 81 , 82 …….

6. HEXADECIMALNUMBER SYSTEM
• Number system has 16 digits. Base is 16
• In this system the first 10 digits are the digits of a
decimal system 0,1,2,3,4,5,6,7,8,9
• The remaining six digits are denoted by
A,B,C,D,E,F representing the decimal values
10,11,12,13,14,15 respectively

7. CONVERSION OF DECIMAL
NUMBER TO BINARY
• Find the binary equivalent of (23)10
2 23
2 11 1 LSB
2 5 1
2 2 1
2 1 0
0 1 MSB
(23)10 = (10111)2

8. CONVERSION OF DECIMAL
NUMBER TO OCTAL
(3451)10 = ()8 ?
8 3451
8 438 3 LSB
8 54 6
8 6 6
0 6 MSB
(3451)10 = (6663)8

9. CONVERSION OF DECIMAL
NUMBER TO HEXADECIMAL
(710)10 = ()16 ?
16 710
16 44 6
16 2 12
0 2
(710)10 = (2C6)16

10. CONVERSION OF BINARY
NUMBER TO DECIMAL
(1110101)2 = ()10 ?
(1*26) + (1*25) + (1*24) + (0*23) + (1*22) + (0*21) + (1*20)
64 32 16 0 4 0 1
= 117
(1110101)2 = (117)10

11. CONVERSION OF BINARY
NUMBER TO OCTAL
SHORTCUT METHOD Example:
(1101010)2 = ()8?
001 101 010
1 5 2
(1101010)2
= (152)8
OCTAL NUMBER BINARY
EQUIVALENT
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

12. CONVERSION OF BINARY
NUMBER TO HEXADECIMAL
SHORTCUT METHOD
Example:
(11010011)2 = 1101 0011
D 3
= (D3)16
DECIMAL HEXA
DECIMAL
BINARY
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
DECIMAL HEXA
DECIMAL
BINARY
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111

13. CONVERSION OF OCTAL
NUMBER TO DECIMAL
Example:
(325)8 = ()10 ?
(3*82) + (2*81) + (5*80)
3*64 + 2*8 + 5*1
192 + 16 + 5
= 213
(325)8 = (213)10

14. CONVERSION OF OCTAL
NUMBER TO BINARY
SHORTCUT METHOD
(6751)8 = ( )2 ?
68 = 110
78 = 111
58 = 101
18 = 001
Hence (6751)8 = (110111101001)2

15. CONVERSION OF OCTAL
NUMBER TO HEXADECIMAL
(125)8 =( )16 ?
Step 1 : convert octal number to decimal
(1*82) + (2*81) + (5*80)
64 + 16 + 5
= 85
Step 2 : convert decimal number to hexadecimal
16 85
16 5 5
0 5
(125)8 = (55)16

16. CONVERSION OF HEXADECIMAL
NUMBER TO DECIMAL
(34F)16 = ( )10 ?
(3*162) + (4*161) + (F*160)
(3*256) + (4*16) + (15*1)
768 + 64 + 15
= 847
(34F)16 = (847)10

17. CONVERSION OF HEXADECIMAL
NUMBER TO BINARY
(ABC)16 = ( )2 ?
A B C
1010 1011 1100
(ABC)16 = (101010111100)2

18. CONVERSION OF HEXADECIMAL
NUMBER TO OCTAL
(C1)16 = ( )8 ?
(C*161) + (1*160)
(12*16) + (1*1)
192 + 1 = 193 (decimal form)
8 193
8 24 1
8 3 0
0 3
(C1)16 = (301)8

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