L33_Fri_Apr_09

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 MAE3811–Sp. 2010 Mahoney–4 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 MAE3811–Sp. 2010 Mahoney–5 Modular Arithmetic, n = 5 Examples: MAE3811–Sp. 2010 Mahoney–6 Modular Arithmetic, n=5, The Full Operation Tables Observations: 4 MAE3811–Sp. 2010 Mahoney–7 Modular Arithmetic, n = 6 Examples: MAE3811–Sp. 2010 Mahoney–8 Modular Arithmetic, n=5, The Full Operation Tables Observations:...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online