1. Presentation on Number System

2. Types of Number System Non-Positional number system

3. Non-Positional Number System
Symbol represents the value regardless of its position.
Difficult to perform arithmetic operation.
For example:-
I, II, III, IV, V, VI, VII, VIII, IX, X XI,XII, XIII, XIV, XV, XVI, XVII,
XVIII, XIX, XX

4. Positional Number System
Symbols represent different values depending upon the position.
The values of each digit is determined by:-
- Digit itself
- Position of the digit
- Base of the number system

5. Decimal number
The base is equal to 10
Uses 10 different symbols.

6. Continue… =2000 + 500 + 80 + 6 =2586 For example:
(2*1000) + (5*100) + (8*10) + (6*1) =
=2586

7. Bit Binary digit 0 or 1 Smallest possible unit of data
Work with a group of bits.

8. Byte
Group of eight bits
Used to represent one character

9. Binary Number System The base is 2.
Each position represents a power of the base 2.
For example:-Conversion from to decimal is-

10. Octal Number System The base is 8 Largest single digit is 7
For example:- decimal equivalent to the octal number 421 is 273

11. Hexadecimal Number System
The base is 16
Combination of 0-9 and A-F
For example:-Decimal equivalent to the hexadecimal number 1421 is 1057

12. Decimal, binary and hexadecimal representations

13. Conversion of decimal representation to binary
Determine the binary equivalent of 3610 2 36 18 9 4 1
Remainder 1
Least Significant Bit (LSB)
Most significant Bit (MSB)

14. Continue…
Taking remainders in reverse order, we have

15. Conversion of binary representation to decimal
= = 26

16. Conversion of hexadecimal to binary
Each hexadecimal digit is equivalent to 4 binary digits.
For example:-binary equivalent to 2C :- C =
2C = (in binary)

17. Conversion binary to hexadecimal
The binary digits are arranged in groups of 4 starting from the right.
For example:-Convert to hexadecimal
( ) 2 = (346 )16

18. Conversion of decimal representation to hexadecimal
(5112)10
Remainder
8 = 8
15=F
3=3
1=1 16
5112
319 19 1
Least significant bit (LSB)
Most significant bit (MSB)
(5112)10=(13F8)16

19. Conversion of hexadecimal representation to decimal
B 6 E
11*256
+ 6*16
+14*1
= = (2926) 10

20. Conversion of octal representation to hexadecimal
Convert each octal digit to 3-bit binary form
Combine all the 3 bits binary form
Divide the binary numbers into the 4-bit binary form
Convert these 4 bits blocks into their respective hexadecimal symbols

21. Continue… Example (2327)8 2 3 7 Octal Number Binary Coded value 010
011
111
Combining 3-bit blocks we have
Dividing of binary numbers into 4-bit binary blocks and
converting these blocks into their respective hexadecimal symbols,
we have:
4 D 7

22. Conclusion
Same procedure to convert decimal numbers to binary, octal & hexadecimal
Same procedure to convert from binary, octal & hexadecimal to decimal numbers