Lec_32_ESC102N_NumberingSystem

Lec_32_ESC102N_NumberingSystem - NumberingSystem Decimal...

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10/19/2010 Lecture 32 1 Numbering System 2 1 0 10 3 10 2 , 10 4 324 : 10 ) 10 ( 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 , 0 : weights Positional Example system numbering Base it Call number a represent to symbols total symbols Use System Numbering Decimal
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10/19/2010 Lecture 32 2 Numbering System 10 3 2 1 0 1 2 0 1 2 124 . 324 exp 10 4 10 2 10 1 10 4 10 2 10 3 124 . 324 int 10 4 10 2 10 3 324 number decimal licit more be To x x x x x x say eger not is number If x x x - - - + + + + + = + + =
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10/19/2010 Lecture 32 3 Binary numbering system system numbering Base called also is system Numbering Total symbols Use system numbering Binary 2 ) 2 ( 1 , 0 :
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10/19/2010 Lecture 32 4 Binary numbering system 10 3 2 1 0 1 2 3 10 0 1 2 3 875 . 13 2 1 2 1 2 1 2 1 2 0 2 1 2 1 111 . 1101 111 . 1101 13 2 1 2 0 2 1 2 1 1101 . 1101 = + + + + + + = = + + + = - - - x x x x x x x have we of case the For x x x x position to assigned weights of terms In say number binary Consider
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10/19/2010 Lecture 32 5 Binary numbering system ) 5 ( 11111 31 ) ( 1 0 2 / 1 1 1 2 / 3 1 3 2 / 7 1 7 2 / 15 ) ( 1 15 2 / 31 31 2 10 10 number bit MSB remainder say number binary to number decimal of Conversion = = = = = =
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10/19/2010 Lecture 32 6 Binary numbering system 2 10 10
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