Introduction to binary number system
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This document discusses different number systems used in digital techniques. It defines analog and digital signals, with analog having continuous values and digital having a finite set of discrete values. Four main number systems are covered: decimal with base 10, binary with base 2, octal with base 8, and hexadecimal with base 16. Each system's base, symbols used, examples of representations, and how place values determine a number's value are explained. The document aims to introduce students to number systems and their applications in digital contexts.
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Introduction to binary number system
- 1. DIGITAL TECHNIQUES DR. VIKAS DONGRE HOD ELECTRONICS &TELECOMMUNICATION GOVERNMENT POLYTECHNIC WASHIM (MS) EMAIL: DONGREVJ1@GMAIL.COM M: 9370668979 UNIT:1 NUMBER SYSTEM and Codes Subtopic: Introduction to Number systems
- 2. Course outcome Student will able to… Use relevant number system for the specific applications.
- 3. Learning outcomes…. Student will able to… Define analog and digital signal. Identify the different number system.
- 4. CONTENTS Analog and Digital signals Number System Representation of Numbers of Different Radix
- 5. Analog and digital signals Signals: Signal is define as a physical quantity, which contains some information and which is a function of one or more independent variable. Types of Signals: 1) ANALOG SIGNALS 2) DIGITAL SIGNALS
- 6. Continue…… Analog signal is define as the signal having continuous values. They can have infinite number of different values. Digital signals is define as the signal which has only a finite number of distinct values.
- 7. Comparison of digital and analog signal Sr. No. Parameter Analog Signal Digital Signal 1 Number of values Infinite Finite 2 Nature Continuous Discrete 3 Sources Signal generators, transducers etc. Computers, A to D converters 4 Examples Sine wave, Triangular wave Binary signal
- 8. What is Number System ? A number system defines a set of values to represent quantity. A number system define how a number can be represented using distinct symbols. A number can be represented differently in different systems. For Example: – -There are several systems for representing, counting numbers. – These include the usual base “10” or decimal system : 1,2,3 ,…..10,11,12,..99,100,…
- 9. The BASE of a number system Base or Radix: The number of values that a digit can assume is equal to the base of a system .
- 10. Different Types Of Number System Decimal Number System. Binary Number system Octal Number System. Hexadecimal Number system.
- 11. Different Types of Number System System Base Symbols Used by humans ? Used in computer ? Decimal 10 0,1,2,…..9 Yes NO Binary 2 0,1 No Yes Octal 8 0,1,2,3….7 NO NO Hexadecimal 16 0,1,2,….9, A,B,…….F NO NO
- 12. Decimal Number System. The decimal number system has a base of 10 i.e. it has 10 distinct symbols from 0 to 9 (0,1,2,3,4,5,6,7,8,9). It is a positional value system in which the value of the digit depends on its position. Most significant bit(MSB) Decimal point Least significant bit(LSB) 103 102 101 100 . 10-1 10-2 10-3
- 13. Decimal Number System For example: consider the decimal number 321, where the digit 3 represents hundreds, 1 represents the tens and 2 represents the ones. 321=300+20+1 Here 3 carries the highest weight of the three digits, hence it is the most significant bit (MSB) and 1 carries the least weight of the three digits, hence it is the least significant bit(LSB).
- 14. Binary Number System The Binary number system has a base of 2 i.e. it has 2 distinct symbols from 0 to 1. The 0 and 1 is called as a Bit. Any binary number can be represented by a string of 1’s and 0’s. A group of four binary bits is known as NIBBLE. A group of 8 binary bits known as a byte.
- 15. Binary Number System. The various digit positions in this system have weights as follows: Most significant bit(MSB) Binary point Least significant bit(LSB) For example: 1) consider the Binary number (1011)2 1 0 1 1 (1x23) + (0x22) + (1x21) + (1x20) = 8 + 0 + 2 + 1 = (11)10 23 22 21 20 . 2-1 2-2 2-3
- 16. Binary Number System For example:2) consider the Binary number (1101.101)2 1 1 0 1 . 1 0 = (1x23)+(1x22)+(0x21)+(1x20)+(1x2-1)+(0x2-2) =8+4+0+1+0.5+0.25 =(13.75)10
- 17. Octal Number System The Octal number system has a base of 8 i.e. it has 8 distinct symbols from 0 to 7 (0,1,2,3,4,5,6,7). The various digit positions in this system have weights as follows: Most significant bit(MSB) Octal point Least significant bit(LSB) 83 82 81 80 . 8-1 8-2
- 18. Octal Number System For example: 1) consider the Octal number (35.7)8 3 5 . 7 (3x81) + (5x80) + (7x8-1) = 24 + 5 + 0.875 = (29.875)10
- 19. Hexadecimal Number System The Hexadecimal number system has a base of 16 i.e. it has 16 distinct symbols from 0 to 9, A to F (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). The various digit positions in this system have weights as follows: Most significant bit(MSB) Hexadecimal point Least significant bit(LSB) 162 161 160 . 16-1 16-2
- 20. Hexadecimal Number System For example: 1) consider the Hexadecimal number (11A.62)16 1 1 A . 6 2 (1x162) + (1x161) + (Ax160) + (6x16-1) + (2x16-2) = (1x256) + (1x16) + (10x1) + (6/16) + (2/256) = 256 + 16 + 10 + 0.375 + 0.0078 = (282.382)10
- 21. Counting Decimal Binary Base 4 Octal Hexadecimal 0 0000 00 00 0 1 0001 01 01 1 2 0010 02 02 2 3 0011 03 03 3 4 0100 10 04 4 5 0101 11 05 5 6 0110 12 06 6 7 0111 13 07 7 8 1110 20 10 8 9 1001 21 11 9 10 1010 22 12 A 11 1011 23 13 B 12 1100 31 14 C 13 1011 31 15 D 14 1100 32 16 E 15 1111 33 17 F
- 22. summary Analog and Digital signals What is number system Different types of number systems
- 23. Thank You !