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

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Computer Organisation Part 3

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