lecture6_7

lecture6_7 - Discrete Computation Structures CSE 2353 Bhanu...

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Discrete Computation Structures CSE 2353 Bhanu Kapoor, PhD Department of Computer Science & Engineering Southern Methodist University, Dallas, TX bkapoor@smu.edu , 214-336-4973 September 15&17, 2009 Embrey 129, SMU, Dallas, Texas Lecture 06, 07 1
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Lecture 06 and 07 Agenda ± Integers ± GCD Algorithm, Prime Numbers ± Mathematical Induction 2
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Integers: Learning Objectives ± Learn about the basic properties of integers ± Division Algorithm teger Representation in Computers ± Integer Representation in Computers ± GCD Algorithm ± Learn about Prime Numbers ± Prime Number Testing athematical Induction ± Mathematical Induction 3
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Integers 4
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Integers ± The div and mod operators ² div iv the quotient of nd btained by ± a div b = the quotient of a and b obtained by dividing a on b. ± Examples: div 5 = 1 ² 8 div 5 = 1 ² 13 div 3 = 4 ² mod od = the remainder of nd btained ± a mod b the remainder of a and b obtained by dividing a on b ² 8 mod 5 = 3 ² 13 mod 3 = 1 5
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Integers 6
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. GCD Algorithm 7
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Extended Euclid d = xa + yb; Given a, b then find d, x, and y 8
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Extended Euclid 9
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Integers ± Relatively Prime Number 10
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Integers ± Least Common Multiples 11
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Representation of Integers ± Decimal System or Base-10 ² The digits that are used to represent numbers in base 10 are 0,1,2,3,4,5,6,7,8, and 9 ± Binary System or Base-2 omputer memory stores numbers in machine ² Computer memory stores numbers in machine language, i.e ., as a sequence of 0s and 1s ± Octal System or Base-8 ² Digits that are used to represent numbers in base 8 are 0,1,2,3,4,5,6, and 7 ± Hexadecimal System or Base-16 eade c aS y s te o a se 6 ² Digits and letters that are used to represent numbers in base 16 are 0,1,2,3,4,5,6,7,8,9, A , B , C D E and F , , , 12
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Representation of Integers 13
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Representation of Integers 14
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Representation of Integers ± Two’s Complements and Operations on
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lecture6_7 - Discrete Computation Structures CSE 2353 Bhanu...

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