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# Computer Organisation Part 3

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Computer Organisation by Mukesh Upadhyay from Lachoo Memorial College Jodhpur

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### Computer Organisation Part 3

1. 1. 01001001000001001001001000100010010000100101111010101010100101010100101001010100100100000100100100100010001001000010010111101010101010010101010010100101001001010010010000010010010010001000100100001001011110101010101001010101001010010101001001000001001001001000100010010000100101111010101010100101010100101001010100100100000100100100100010001001000010010111101010101010010101010010100101010010010000010100100100000100100100100010001001000010010111101010101010010101010010100101010010010000010010010010001000100100001001011110101010101001010101001010010100100100100010001001000010010111101010101010010101010010100101010010010000010010010010001000100100001001011110101010101001010101001010010101001001000001001001001000100010010000100101111010101010100101010100101001010010000010010010010001000100100011001011110101010101001010101001010010110010010000010010010010001000100100001001011110101010101001010101001010010101001001000001001001001000100010010000100101111010101010100101010100101001010100100100000100100<br />Number system<br />Simplicity of complexity<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
2. 2. NUMBERS<br />FIXED POINT<br />FLOATING POINT<br />REAL NUMBERS<br />FLOATING<br />POINT<br />Number means, Value assigned to a particular symbol.<br />35<br />Tens Unit<br />3 X 10 + 5 X 1<br />23.45<br />Whole Part Fractional Part <br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
3. 3. 23.4500 X 100<br />234.500 X 10-1<br />2345.00 X 10-2<br />2.34500 X 101<br />.234500 X 102<br />Representation of Floating Point Number : <br />+/- m X b+/-e<br />exponent<br />mantissa<br />base<br />.<br />power<br />.<br />power<br />( Therefore, it is floating point )<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
4. 4. Arithmetic Operation :<br />Addition and Subtraction <br /> i.) make e1 = e2<br /> ii.) Add/Subtract m1 and m2<br /> Example :<br /> N1 N2<br /> 29.32 2.48<br /> 29.32 X 100 2.48 X 100<br /> 2.932 X 101 .248 X 101<br /> 2.932 X 101<br /> .248 X 101<br /> --------------------------<br />3.580 X 101<br /> --------------------------<br />Multiplication <br /> i.) Add e1 = e2<br /> ii.) Multiply m1 and m2<br />Division <br /> i.) Subtraction e1 = e2<br /> ii.) Divide m1 and m2<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
5. 5. Normalization of Numbers : <br />After decimal there is always non zero value than representation<br />is called NORMALIZED<br />But, ZERO can not be normalized, because zero <br />can not contain any non zero value therefore it is so.<br />For –ve<br />0 For +ve<br />__ . __ __ __ __ __ __ __ __ __ __ __<br />m<br />Exp<br />sign<br />sign<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
6. 6. Errors are of 2 types : <br /> 1.) Truncation Error<br /> .0003899  .00038<br /> here,<br /> 99 X 10-7<br /> 2.) Round off Error<br /> .0003899  .00039<br /> here,<br /> 99 X 10-7<br /> In both the above cases there is intolerable. Therefore we go for <br />After decimal there is always non zero value than representation<br />is called NORMALIZED<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
7. 7. Examples :<br /> .0003899  .3899000 X 10-3 <br /> 0 3 8 9 9 0 1 0 3 <br />+ . 3 8 9 9 0 - 1003<br /> 235.8  .2358 X 103 <br /> 0 2 3 5 8 0 0 0 4 <br /> 1 9 9 9 9 9 0 0 2 <br />+ . 3 8 9 9 0 + 1003<br /> 99.999  .99999 X 102 <br />- . 9 9 9 9 9 + 1002<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
8. 8. Examples :<br /> -.00836  .836 X 10-2 <br /> 1 8 3 6 0 0 1 0 2 <br />- . 3 8 9 9 0 - 1002<br /> -00235.7  .23587 X 105 <br /> 1 2 3 5 8 7 0 0 5 <br /> 1 9 9 9 9 9 1 0 2 <br />- . 2 3 5 8 7 + 1005<br /> -.00999  .99999 X 10 -2 <br />- . 9 9 9 9 9 - 10 -02<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
9. 9. +/- m X b +/-e<br />23<br />8<br />1<br />IEEE 754 Standard :<br />Double<br />Single<br />for exponent<br />biased value 127 (default number)<br />EXPONENT<br />MANTISSA<br />32<br />32 bits because it is decided in standard in 1EEE 754 floating point standard<br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
10. 10. Examples<br />(11)10<br />(1)10<br />0<br />0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0<br />1 1 1 1 1 1 1 1 <br />Krishna Kumar Bohra (KKB), MCA LMCST<br />www.selectall.wordpress.com<br />
11. 11. Ccontd…<br />