Data r epresentation
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Data r epresentation

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Sanjeev Patel 4x

Sanjeev Patel 4x

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Data r epresentation Data r epresentation Presentation Transcript

  • DATA REPRESENTATION
    BY-
    Ravi Sharma
  • Binary number system- [ 0and 1 ] Radix-2 , e.g.-(101101)2
    Decimal number system- [ 0 to 9 ] Radix-10 , e.g.-(243)10
    Octal number system- [ 0 to 7 ] Radix-8 , e.g.-(736.4)8
    Hexadecimal - [ 0 to 9 and A to F ]
    Radix-16, e.g.-(F3)16
    NUMBER SYSTEMS:
  • Conversion to decimal-
    A number expressed in base r can be converted to its decimal equivalent by multiplying each coefficient by corresponding power of r and adding . The following is an example of octal to decimal conversion:
    Conversion
  • Conversion from decimal to ‘r’ :
    Conversion of decimal integer into a base r is done by successive divisions by r and accumulation of the remainders . The conversion of fraction is done by successive multiplication by r and accumulation of integer so obtained.
  • Conversion from and to binary , octal , hexadecimal-
    Since 23=8 and 24=16, each octal digits corresponds to three and each hexadecimal corresponds to 4 binary digits . The conversion from binary to octal and hexadecimal is done by partitioning the binary no. into groups of three and four bits respectively .
  • (r-1)’s -
    - 9’s complement :
    It follows that the 9’s complement of a decimal no. is obtained by subtracting each digit from 9.
    e.g.- 9’s complement of 546700 is 999999-546700=453299
    -1’s complement:
    The 1’s complement of a binary no. is obtained by subtracting each digit by 1.
    e.g.- 1’s complement of 1011001 is 0100110.
    Complements
  • ( r’s ) –
    -10’s complement :
    10’s complement of a decimal number is obtained by adding 1 to the 9’s complement value.
    e.g.- 10’s complement of 2389 is 7610+1=7611.
    -2’s complement :
    2’s complement of binary number is obtained by adding 1 to the 1’s complement.
    e.g. – 2’s complement of 101100 is 010011+1=010100.
  • Subtraction of unsigned numbers
  • Signed Numbers
  • An overflow condition can be detected by observing the carry into the sign bit position and carry out of the sign bit position . If these two carries are not equal an overflow is occurred .
    carries: 0 1 carries: 1 0
    +70 0 1000110 -70 1 0111010
    +800 1010000-801 0110000
    +150 1 0010110 -150 0 1101010
    Overflow
  • THANK YOU
    THANK YOU