CS101.Lect11.BinaryNumbers.ppt

CS101.Lect11.BinaryNumbers.ppt - CS101 Lecture 11: Binary...

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Computer Science CS101 Lecture 11: Binary Numbers Number Systems Binary Numbers Hexadecimal Aaron Stevens ([email protected]) 4 October 2011 Computer Science
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Computer Science Computer Science TODAY’S LECTURE CONTAINS TRACE AMOUNTS OF ARITHMETIC AND ALGEBRA PLEASE BE ADVISED THAT CALCULTORS WILL BE ALLOWED ON THE QUIZ (and that you probably won’t need them) !!! MATH WARNING !!!
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Computer Science Overview/Questions What gives a number its value? What is a number system? I’ve heard that computers use binary numbers. What’s a binary number? What kind of numbers do computers store and manipulate? Computer Science 2 Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645, 32 Negative Numbers A value less than 0, with a – sign Examples: -24, -1, -45645, -32 Numbers
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Computer Science 3 Integers A natural number, a negative number, zero Examples: 249, 0, -45645, -32 Rational Numbers An integer or the quotient of two integers Examples: -249, -1, 0, 3/7, -2/5 Numbers Computer Science 4 A numbering system assigns meaning to the position of the numeric symbols. For example, consider this set of symbols: 642 What number is it? Why? Numbering Systems
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Computer Science 5 It depends on the numbering system. 642 is 600 + 40 + 2 in BASE 10 The base of a number determines the number of digits (e.g. symbols) and the value of digit positions Numbering Systems Computer Science 6 Continuing with our example… 642 in base 10 positional notation is: 6 x 10 2 = 6 x 100 = 600 + 4 x 10 1 = 4 x 10 = 40 + 2 x 10º = 2 x 1 = 2 = 642 in base 10 This number is in base 10 The power indicates the position of the number Positional Notation
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7 d n * B n-1 + d n-1 * B n-2 + . .. + d 1 * B 0 As a general form: 642 = 6 3 * 10 2 + 4 2 * 10 1 + 2 1 * 10 0
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This note was uploaded on 12/16/2011 for the course CS 101 taught by Professor Stevens during the Fall '08 term at BU.

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CS101.Lect11.BinaryNumbers.ppt - CS101 Lecture 11: Binary...

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