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Aravali College of Engineering and Management, Faridabad

binary and decimal Number System

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Aravali College of Engineering and Management, Faridabad

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  1. NumberSystem Program Name : BBA (FS&B)Semester : 1st Sem Course Name: Computer & Information Systems Course Code : BBA/II/104

  2. What is Number System? • A system for representing number of certain type. • A number system defines a set of values used to representquantity. • Example: • –There are several systems for representing the countingnumbers. • –These include the usual base “10” or decimal system :0,1,2,3,…..10,11,12,..99,100,…

  3. NumberSystem • Decimal is the number system and is used in our day to daylife • Binary is a number system that is used incomputers • Octal is a number system that represents groups of binary numbers. It is used in digitaldisplays. • Hexadecimal (Hex) is a number system that represents groups of binary numbers. Hex is primarily used incomputing.

  4. Different NumberSystem • Decimal NumberSystem • -Base10 • Binary NumberSystem • Base2 • Octal NumberSystem • -Base8 • Hexadecimal Number System • Base16

  5. Common NumberSystem Used in computers ? Used by humans? System Base Symbols decimal A, B, …F

  6. Counting Hexa- decimal

  7. Decimal NumberSystem • Decimal number system contains ten unique symbols 0,1,2,3,4,5,6,7,8 and9. • Since counting in decimal involves ten symbols, we can say that its base or radix isten. • In this system, any number (integer, fraction or mixed) of any magnitudecan • be represented by the use of these ten symbolsonly • Each symbols in the number is called a“Digit” • Examples • 1214 • 1897 • 9875.54

  8. Binary NumberSystem • Binary number system is a positional weightedsystem. • It contains two unique symbols 0 and1. • Since counting in binary involves two symbols , we can say that its base or radix istwo. • A binary digit is called a“Bit” • A binary number consists of a sequence of bits, each of which is either a 0 or a1. • The binary point separates the integer and fraction parts. • Examples, 1110 • 0000 • 1001 • 0101

  9. Octal NumberSystem • Octal number system is a positional weightedsystem. • It contains eight unique symbols 0,1,2,3,4,5,6 and7. • Since counting in octal involves eight symbols, we can say that its base or radix iseight. • The largest value of a digit in the octal system will be7. • That means the octal number higher than 7 will not be 8, instead of that it will be10

  10. Hexadecimal NumberSystem • Binary numbers are long. These numbers are fine for machines but are too lengthy to be handled by human beings. So there is a need to represent the binary numbers concisely. • One number system developed with this objective is the hexadecimal number system (orHex) • It contains sixteen uniquesymbols • 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E andF. • Since counting in hex involves sixteen symbols, we can say that its base or radix issixteen.

  11. BCD or 8421Numbers • BCD means Binary CodedDecimal. • BCDisasystemofweitinganumbersthat a four-digit binary code to each digit 0 through 9 in decimalnumbers. • The smallest BCD number is (0000) and the largest is (1001). The next number to 9 will be 10 which is expressed as (0001 0000) inBCD. • There are six illegal combinations 1010, 1011,1100, 1101, 1110 and 1111 in this code i.e. they are not part of the 8421 BCDcode

  12. Decimal to BCDconversion Sr.No. DecimalNumber BCD

  13. First Conversion

  14. Second conversion

  15. Aravali College of Engineering And Management Jasana, Tigoan Road, Neharpar, Faridabad, Delhi NCR Toll Free Number : 91- 8527538785 Website : www.acem.edu.in

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