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CS101.Lect11.BinaryNumbers

CS101.Lect11.BinaryNumbers - CS101 Lecture 11 Number...

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1 1 Aaron Stevens 14 February 2011 CS101 Lecture 11: Number Systems and Binary Numbers 2
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2 3 4 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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3 5 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? 6 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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4 7 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 8 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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5 9 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 10 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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6 11 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 B is the base n is the number of digits in the number
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