Fractions - BinaryFractions Fractions A radix separates the...

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Binary Fractions
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Fractions A radix separates the integer part from the fraction part of a number. 101.101 Columns to the right of the radix have negative powers of 2.
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Fractions 2 2 2 1 2 0 . 2 -1 2 -2 2 -3
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Fractions 2 2 2 1 2 0 . 2 -1 2 -2 2 -3 4 2 1 . ½ ¼
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Fractions 2 2 2 1 2 0 . 2 -1 2 -2 2 -3 4 2 1 . ½ ¼ 1 0 1 . 1 0 1
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Fractions 2 2 2 1 2 0 . 2 -1 2 -2 2 -3 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 4 + 1 + ½ +
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Fractions 2 2 2 1 2 0 . 2 -1 2 -2 2 -3 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 4 + 1 + ½ + 5⅝
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Fractions Another way to assess the fraction: 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 Just as this is 5
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Fractions Another way to assess the fraction: 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 Just as this is 5 so is this!
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Fractions Another way to assess the fraction: 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 Just as this is 5 so is this Except it’s not 5 ones. It’s 5 eighths.
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Fractions Another way to assess the fraction: 4 2 1 . ½ ¼ 1 0 1 . 1 0 1 Just as this is 5 so is this Except it’s not 5 ones. It’s 5 eighths.
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Fractions But there’s no dot (.) in Binary! We need to explore a method for storing fractions without inventing another symbol.
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Scientific Notation Very large and very small numbers are often represented such that their orders of magnitude can be compared. The basic concept is an exponential notation using powers of 10. a × 10 b Where b is an integer, and a is a real number such that: 1 ≤ |a| < 10
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examples An electron's mass is about 0.00000000000000000000000000000091093826 kg. In scientific notation, this is written:
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This note was uploaded on 04/06/2012 for the course CSE 1520 taught by Professor Kemeny during the Spring '08 term at York University.

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Fractions - BinaryFractions Fractions A radix separates the...

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