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# Chapter 7 rohith

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Basic Electronics Notes

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### Transcript of "Chapter 7 rohith"

1. 1. Basic Electronics Notes Number system UNIT-VII Syllabus 1. NUMBER SYSTEMS: Introduction, decimal system, Binary, Octal and Hexadecimal number systems, addition and subtraction, fractional number, Binary Coded Decimal numbers. NUMBER SYSTEM The human need to count things goes back to the dawn of civilization. To answer the questions like how much or how many‖, people invented number system. A number system is any scheme used to count things. The decimal number system succeeded because very large numbers can be expressed using relatively short series of easily memorized numerals. Decimal or base 10 number system‘s origin: can be traced to, counting on the fingers with digits. In any number system, the important term is Base or radix Base: Base is the number of different digits or symbols or numerals used to represent the number system including zero in the number system. It is also called the radix of the number system. Commonly used number systems : 1. Decimal 2. Binary 3. Octal 4. Hexadecimal. Decimal number system : The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Using these symbols as digits of a number, we can express any quantity. The decimal system is also called the base-10 system because it has 10 digits. Binary number system : In the binary system, there are only two symbols or possible digit values, 0 and 1. This base-2 system can be used to represent any quantity that can be represented in decimal or other base system Octal number system : The octal number system has a base of eight, meaning that it has eight possible digits: 0,1,2,3,4,5,6,7. The octal numbering system includes eight base digits (0-7).After 7, the next placeholder to the right begins with a “1” i.e 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13 ... Hexadecimal number system: The hexadecimal system uses base 16. Thus, it has 16 possible digit symbols. It uses the digits 0 through 9 plus the letters A, B, C, D, E, and F ,to represent 10 through 16, as the 16 digit symbols Digits = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F} Rohith.S, Asst. Professor, NCET, Bangalore Page 1
2. 2. Basic Electronics Notes Number system Conversion of number systems. Converting from one number system to another is called conversion of number system or code conversion, like converting from binary to decimal or converting from hexadecimal to decimal etc. Procedure for Conversion from One Number system to Other Number systems Number system Number Procedure (From) system (To)  Multiply each bit by 2n, where n is the “weight” of the bit Binary Decimal  Hexadecimal Add the results Group every 4 bits and represent it into Hexadecimal using table  Group every 3 bit and Represent it into octal using table Binary   Divide by two, keep track of the remainder Group the remainders from Bottom to Top Hexadecimal  Repeated division by 16 and Keep track of the Reminder. Octal  Repeated division by 8 and Keep track of the Reminder. Binary  Represent each digit by group of 3 bits as given in table Decimal  Multiply each digit by 8n, where n is the “weight” of the bit  The weight is the position of the bit, starting from 0 on the right  Add the results  Convert Octal to Binary first.  Regroup the binary number by four bits per group starting from LSB  Use the table to represent the digit Binary  Represent each digit by group of 4 bits Decimal  Multiply each bit by 16n, where n is the “weight” of the bit  The weight is the position of the bit, starting from 0 on the right  Add the results  Convert Hexadecimal to Binary first.  Regroup the binary number by three bits per group starting from LSB.  Octal   Octal Decimal The weight is the position of the bit, starting from 0 on the right Use the table to represent the digit Hexadecimal Hexadecimal Octal Rohith.S, Asst. Professor, NCET, Bangalore Page 2
3. 3. Basic Electronics Notes Octal –To- Binary / Binary- To- Octal Conversion Octal 0 1 2 3 Digit Binary 000 001 010 011 Equivalent Number system 4 5 6 7 100 101 110 111 5 6 7 0101 0110 0111 D E F 1101 1110 1111 Binary-To-Hexadecimal /Hexadecimal-To-Binary Conversion Hexadecimal 0 1 2 3 4 Digit Binary 0000 0001 0010 0011 0100 Equivalent Hexadecimal 8 9 A B C Digit Binary 1000 1001 1010 1011 1100 Equivalent Subtraction Using Number System Complement method of subtraction The complement method of subtraction is the method used for subtraction of numbers in different number systems. This method is useful as it can easily implemented in arithmetic logic circuits and inverting circuits in computers. The complement method used in various no. systems discussed above is indicated below: For decimal system – 9‘s complement method – 10‘s complement method For binary system – 1‘s complement method -- 2‘s complement method For octal system – 7‘s complement method – 8‘s complement method For hexadecimal system – 15‘s complement method – 16‘s complement method For subtraction of two numbers we have two cases : 1 Subtraction of smaller number from larger number 2 Subtraction of larger number from smaller number Subtraction Using Binary no. System The 1‘s complement of a given binary no. is the new no. obtained by changing all the 0‘ to 1, and all 0‘s to 1 Ex : 11010‘s 1‘s complement is 00101 Rohith.S, Asst. Professor, NCET, Bangalore Page 3