L33_Fri_Apr_09 - number if that number is bigger than the...

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1 MAE3811–Sp. 2010 Mahoney–1 Wrapping the Integers around the Clock Last time we saw that the clock, with its special clock addition, behaved like the integers. Both are _____________ because you can do simple algebra on them both. We can wrap the integers around the clock like this… In a sense we can say that the certain integers are equivalent ( _________ ) to numbers on the clock. Example. MAE3811–Sp. 2010 Mahoney–2 Modular Congruence For integers a and b, a is ______________ to b __________________ m , written If and only if, a – b is a ________________ of m, where m is a positive integer greater than 1. Said another way, Examples: 23 = ____ ( mod 12 ) -45 = ____ ( mod 12 ) b harder than normal so check
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2 MAE3811–Sp. 2010 Mahoney–3 Modular Congruence Continued This works for any modulus, not just 12 Examples: 98 = ____ ( mod 5) 45 = ____ ( mod 3 ) Often a number followed by “(mod a)” means to calculate the equivalent modulus
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Unformatted text preview: number if that number is bigger than the modulus. For example. 13 ( mod 12) means __________ because . .. Algorithm for calculating Modulo: Divide the number by the modulus, the remainder is the answer The remainder is usually positive and less than the modulus MAE3811Sp. 2010 Mahoney4 Modular Arithmetic The n-modular integers are the numbers And have at least two operations defined by How do you think modular subtraction and modular division are defined? 3 MAE3811Sp. 2010 Mahoney5 Modular Arithmetic, n = 5 Examples: MAE3811Sp. 2010 Mahoney6 Modular Arithmetic, n=5, The Full Operation Tables Observations: 4 MAE3811Sp. 2010 Mahoney7 Modular Arithmetic, n = 6 Examples: MAE3811Sp. 2010 Mahoney8 Modular Arithmetic, n=5, The Full Operation Tables Observations:...
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L33_Fri_Apr_09 - number if that number is bigger than the...

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