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- 1. DATA REPRESENTATION<br />BY-<br /> Ravi Sharma<br />
- 2. Binary number system- [ 0and 1 ] Radix-2 , e.g.-(101101)2<br />Decimal number system- [ 0 to 9 ] Radix-10 , e.g.-(243)10<br />Octal number system- [ 0 to 7 ] Radix-8 , e.g.-(736.4)8<br />Hexadecimal - [ 0 to 9 and A to F ]<br /> Radix-16, e.g.-(F3)16<br />NUMBER SYSTEMS:<br />
- 3. Conversion to decimal-<br />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:<br />Conversion<br />
- 4. Conversion from decimal to ‘r’ :<br /> 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.<br />
- 5. Conversion from and to binary , octal , hexadecimal-<br />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 .<br />
- 6. (r-1)’s -<br /> - 9’s complement : <br />It follows that the 9’s complement of a decimal no. is obtained by subtracting each digit from 9.<br /> e.g.- 9’s complement of 546700 is 999999-546700=453299<br /> -1’s complement:<br />The 1’s complement of a binary no. is obtained by subtracting each digit by 1.<br /> e.g.- 1’s complement of 1011001 is 0100110.<br />Complements<br />
- 7. ( r’s ) –<br />-10’s complement : <br /> 10’s complement of a decimal number is obtained by adding 1 to the 9’s complement value.<br /> e.g.- 10’s complement of 2389 is 7610+1=7611.<br />-2’s complement : <br />2’s complement of binary number is obtained by adding 1 to the 1’s complement.<br />e.g. – 2’s complement of 101100 is 010011+1=010100.<br />
- 8. Subtraction of unsigned numbers<br />
- 9. Signed Numbers<br />
- 10.
- 11. 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 .<br />carries: 0 1 carries: 1 0<br /> +70 0 1000110 -70 1 0111010<br />+800 1010000-801 0110000 <br />+150 1 0010110 -150 0 1101010<br />Overflow<br />
- 12. THANK YOU<br />THANK YOU<br />

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