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.
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