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Various num systems used in digital comp.18to19
 

Various num systems used in digital comp.18to19

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    Various num systems used in digital comp.18to19 Various num systems used in digital comp.18to19 Presentation Transcript

    • Various number system used in digitalcomputers http://improvec.blogspot.in/ 1
    • Recap:Number systemsImportance of binary number system http://improvec.blogspot.in/ 2
    • PrerequisiteWhat are various number systems used incomputers? Binary number system. Octal number system. Hexadecimal number system. http://improvec.blogspot.in/ 3
    • DECIMAL NUMBER SYSTEM http://improvec.blogspot.in/ 4
    • Decimal number system: The number system that we use in our daily life is called the decimal number system. The decimal number system is a base-10 system. It uses 10 digits, from 0 to 9. http://improvec.blogspot.in/ 5
    • Decimal number system (contd...) : Example – (1234)10 subscript 10 denotes decimal number. The base or radix of a number system is defined as the number system uses ten digits. The weight of each digit of a decimal number depends on its relative position within the number. http://improvec.blogspot.in/ 6
    • Weight of each digit of a decimal number: 6498 = 6000 + 400 + 90 + 8 = 6*103 + 4*102 + 9*101 + 8*100 The weight of the 1st digit of the number from right handside = 1st digit * 100 The weight of the 2nd digit of the number from right handside = 2nd digit * 101 http://improvec.blogspot.in/ 7
    • Weight of each digit of a decimal number (contd) : The weight of the 3rd digit of the number from right handside = 3rd digit * 102 The weight of the 4th digit of the number from right handside = 4th digit * 103 http://improvec.blogspot.in/ 8
    • Weight of each digit of a decimal number (contd) :General expressionThe weight of the nth digit of the number from right hand side = nth digit * 10n-1 = nth digit * (Base)n-1 http://improvec.blogspot.in/ 9
    • BINARY NUMBER SYSTEM http://improvec.blogspot.in/ 10
    • Binary number system: Binary number system is used in digital computers. The base (or radix) of binary system is 2. It uses only two digits 0 or 1 and these digits are abbreviated as bits. http://improvec.blogspot.in/ 11
    • Binary number system (contd) : Example – (11010)2 = (26)10 The weight of each digit of a binary number depends on its relative position within the number. http://improvec.blogspot.in/ 12
    • Weight of each bit of a binary number: 1101 (binary number) = 1*23 + 1*22 + 0*21 + 1*20 =8+4+0+1 = 13 (decimal number) The weight of the 1st bit of the binary number from right hand side = 1st bit * 20 The weight of the 2nd bit of the number from right hand http://improvec.blogspot.in/ 13 side = 2nd bit * 21
    • Weight of each bit of a binary number (contd) : The weight of the 3rd bit of the number from right handside = 3rd bit * 22 The weight of the 4th bit of the number from right handside = 4th bit * 23 http://improvec.blogspot.in/ 14
    • Weight of each bit of a binary number (contd) :General expression The weight of the nth bit of the number from right hand side = nth bit * 2n-1 = nth bit * (Base)n-1 http://improvec.blogspot.in/ 15
    • Binary equivalent of decimal numbers:Decimal No. Binary equal Decimal No. Binary equal0 0 11 10111 01 12 11002 10 13 11013 11 14 11104 100 15 11115 101 16 100006 110 31 111117 111 32 1000008 1000 63 1111119 1001 64 100000010 1010 128 10000000 http://improvec.blogspot.in/ 16
    • OCTAL NUMBER SYSTEM http://improvec.blogspot.in/ 17
    • Octal number system: Octal means 8. The base of octal number system is 8. It uses eight digits 0,1,2,3,4,5,6, and 7. The decimal number 8 is represented by 10, 9 by 11, 10 by 12 and so in octal number system. http://improvec.blogspot.in/ 18
    • Octal number system (contd) : As 8 = 23, each octal digit is represented by a group of three binary bits. This system was issued to provide a shorthand way to deal with long strings of 0s and 1s created in binary. Example – (2056)8 = (1070)10 http://improvec.blogspot.in/ 19
    • Binary representation of octal digits: Decimal Octal number 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 10 10 12 15 17 http://improvec.blogspot.in/ 20
    • Conversion of octal to binary:To convert a binary number to octal. Group binary digits in group of three. Convert each group to its equivalent octal digit. Example – (101110)8= 56 101 110 5 6 http://improvec.blogspot.in/ 21
    • Hexadecimal number system Hexadecimal means 16(6+10) It contains 16 symbols Its base is 16. http://improvec.blogspot.in/ 22
    • Hexadecimal number system (contd) The first ten digits are represented by digits 0 to 9 and remaining six by the letters A through F. Each hexadecimal digit is represented by four binary bits. Example – (A3)16 = (1010 0011)2 http://improvec.blogspot.in/ 23
    • EQUIVALENT VALUES OF DIFFERENT SYSTEMSDECIMAL BINARY OCTAL HEXADECIMAL0 0000 0 01 0001 1 12 0010 2 23 0011 3 34 0100 4 45 0101 5 56 0110 6 67 0111 7 78 1000 10 89 1001 11 910 1010 12 A11 1011 13 B12 1100 14 C13 1101 15 D14 1110 16 E15 1111 17 F16 10000 20 10 http://improvec.blogspot.in/ 24
    • Summary:In this class, you have learnt about Various number systems used in digital computer http://improvec.blogspot.in/ 25
    • Frequently Asked Questions1. What is meant by base of a number system ?2. What is the value of the base for decimal, binary, octal and hexadecimal number systems?3. What are octal and hexadecimal number systems ? http://improvec.blogspot.in/ 26
    • Quiz1. The decimal number system is a a. base 2 b. base 16 c. base 10Answer: c http://improvec.blogspot.in/ 27
    • Quiz2. The base of octal number system is a. 8 b. 16 c. 2Answer: a http://improvec.blogspot.in/ 28
    • Quiz3. The first ten digits in hexa decimal system are represented by digits 0 to 9 and remaining six by the letters a. 10 to 16 b. A to F c. A1 to A6Answer: b http://improvec.blogspot.in/ 29