This document discusses different number systems used in digital electronics including decimal, binary, octal, and hexadecimal. It provides examples of numbers represented in each system and methods to convert between the different bases. Conversion methods covered include converting from binary, octal, or hexadecimal to decimal and vice versa, as well as converting between octal and hexadecimal to binary and back. Examples are given to demonstrate each conversion method.

1. Department of Mechanical Engineering
NIT, ARUNACHAL PRADESH
Number System
(Representation and Conversion)

2. INTRODUCTION :
Number System ?

3. NUMBER SYSTEM IN DIGITAL ELECTRONICS
1. Decimal Number
2. Binary Number
3. Octal Number
4. Hexadecimal
Number
5. BCD Number
6. Excess 3 Code
Used by Humans
Used by Computer
Digital System

4. COMMON NUMBER SYSTEM
Number Base Allowable Digits / Characters Symbol
Decimal (D) 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 … 10
Binary (B) 2 0, 1 … 2
Octal (O) 8 0, 1, 2, 3, 4, 5, 6, 7 … 8
Hexadecimal (H) 16
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E,
F … 16

5. CONVERSION
1. B / O / H  D
2. D  B / O / H
3. O / H  B  H / O
Decimal Hexadecimal Octal Binary
0 0 0 0
1 1 1 1
2 2 2 10
3 3 3 11
4 4 4 100
5 5 5 101
6 6 6 110
7 7 7 111
8 8 10 1000
9 9 11 1001
10 A 12 1010
11 B 13 1011
12 C 14 1100
13 D 15 1101
14 E 16 1110
15 F 17 1111

6. 1. B / O / H  D
(AnAn-1 - - - - A1A0)B (N)10
N = AnBn + An-1Bn-1 + ------ + A2B2 + A1B1 + A0B0
Example
(10101)2 ( )10
(1357)8 ( )10
(A2D)16 ( )10
21
751
2605

7. 2. D  B / O /
H
(N)10 (AnAn-1 - - - - A1A0)B
B N
B N1 A0
- - A1
- - -
- - -
B Nn-1 -
An = Nn An-1
Example
(55)10 ( )2
(55)10 ( )8
(55)10 ( )16
110111
67
37

8. 3. O / H  B  H / O
Example
(473)8 ( )2100111011
(An --- A1A0)8 (an3an2an1 --- a13a12a11 a03a02a01)2
(An --- A1A0)16 (an4an3an2an1 --- a14a13a12a11 a04a03a02a01)2
( )1613B

9. TRY YOURSELF
( )16
( )2
( )10
11111101
( )8
FB
253
375
( )10
( )8
( )2
140336
( )16
49374
1100000011011110
C0DE

10. PROGRAMMING LANGUAGE

11. MACHINE LANGUAGE VS ASSEMBLY LANGUAGE