Ee1032aS10

Ee1032aS10 - Introduction to Base 2 Arithmetic 12 1101 2...

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Introduction to Base 2 Arithmetic 2 10 10 12 1 10 2 10 (12) (.12) 10 10   1 2 3  12 .625 1 10 2 10 6 10 2 10 5 10   02 (12.625) 10 (.12625) 10 10 10 EE103 SLIDES 2A (SEJ) 1 Base 2 32 1 0 1 2 12 0 2 0 2 0 4 (1100) 2 ( 1100) 2 22 (.1100) 1 0 1 2 3 12.625 1 2 1 2 0 2 0 2 1 2 0 2 1 2         04 (1100.101) 2 (.1100101) 2  Base 8 1 12.625 1 8 4 8 5 8 88 (14.5) 8 (.145) 8 EE103 SLIDES 2A (SEJ) 2

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Example of Conversion of a Positive Integer from Base 10 to Base 2 101 2 : Ex Convert to its Base representation 1 101 2 50 1 / 2 50 2 25 0 / 1 25 2 12 1 / 2 12 2 6 0 / 62 3 0 / 1 2 32 1 1 / 1 2 12 0 1 / 7 101 1100101 1100101 2  () ( ) EE103 SLIDES 2A (SEJ) 3 22 . 12 1 0 2 KK K Nd d d d d   Conversion of a Positive Integer from Base 10 to Base 2 1 0 K  3 0 0 1 2 2 K K dd d d  2 NQ d 00 234 01 222 KKK Qd d  K 1 2 QQ d EE103 SLIDES 2A (SEJ) 4 ETC.
Conversion to Base 8 5 8 101 8 12 5 / 4 8 12 8 1 4 / 1 8 18 0 1 / 3 88 101 145 145 8  ()( . ) EE103 SLIDES 2A (SEJ) 5 Convert 0.1 to Base 2 01x 20 2 0 .. 02x2 04 0 04x2 08 0 08x 21 6 1 06x2 12 1 0 ! a repeat 3 22 0 1 0001100110011 1100110011 2  .( . )( . )  01 2 , Thatis does not have a finite Base representation EE103 SLIDES 2A (SEJ) 6

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Conversion of a fraction from base 10 to base 2 01 R  123 222 2 n Rd d d d  12 3 n     1 2( 2 2 2 ) n d d d  3 n 1 22 ( 2 2 2 ) n Fd d d 23 ( ) n n n dd d Etc. EE103 SLIDES 2A (SEJ) 7 mantissa Description of Machine Numbers (. ) e n ddd d  exponent Bas 1 n e k k k d where 0,1,2,. .., 1 d i  and is an integer.  Base min max ee e 1 0 normalized machinenumber d : Largest Machine Number 11 1 1 n   ( . () ) ( ) EE103 SLIDES 2A (SEJ) 8
Geometric Sums 1 0: 1 n n k x x x 0 1 1 k n n k x x xx  1 1 1 1 k nj n kj x x   1 ,1 1 x xj n x   0| | 1 1 lim n kk n for x and x x x

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Ee1032aS10 - Introduction to Base 2 Arithmetic 12 1101 2...

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