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#How do you do division in modular arithmetic how to
#How do you do division in modular arithmetic mod
#How do you do division in modular arithmetic serial

Other examples of check digits algorithms using modulo operations:

#How do you do division in modular arithmetic serial

NPI - US National Provider Identifier use the modulo 10 operation to calculate the tenth digit.Īs the check digits are used to capture human transcription errors, they are often used for long serial numbers.

IBAN - International Bank Accounts Numbers - make use of modulo 97 to check whether a client didn't mistype the number.

ISBN and ISSN numbers, which are unique periodic and book identifiers, have modulo 11 or modulo 10, and an average weighting applied in check digit formula.

The formula for the check digits use modulo 10.

GTIN, UPC, EAN check digits are used to confirm the integrity of a barcode.

You can find the application of modulo in: They are there to inform you about errors arising, e.g., from mistyping. Check digits are used mostly in long numbers, and they are the digits computed by an algorithm.

Modulo operations are used to calculate the checksums of serial numbers.

41 minutes and 30 seconds sounds much better. Nobody will say that "you have 40 minutes and 90 seconds left", right? The only option is to perform a modulo operation and find the quotient and remainder – 60 * 1 + 30 = 90. It may be adding the hours, like in the explanation of modulo above, or minutes, or seconds as well!

The most obvious and well-known example is the so-called clock arithmetic 🕞.

They might not be obvious at first glance, but there are many applications of modulo – from everyday life to math and science problems!

#How do you do division in modular arithmetic mod

If you want to read about them and practice modular arithmetic, check out our dedicated power mod calculator. You can, however, use the multiplication properties to get around this problem:Ģ^100 mod 3 = (2^50 mod 3 * 2^50 mod 3) mod 3Įven faster modular exponentiation methods exist for some specific cases (if B is a power of 2). Unfortunately, our calculator can't handle numbers as big as this due to overflow – only numbers up to 2^60 can be held. So have a look at another problem: we want to calculate the A^B mod C for large values of B – like, e.g., 100. The usefulness of this formula may be not so obvious in this example, as we still need to use the calculator to find the exponentiation result (assuming that you don't know the result of 3^7 immediately).

This formula is even more useful when dealing with large numbers. Right part of the equation: (11 mod 4 * 7 mod 4) mod 4 = (3 * 3) mod 4 = 9 mod 4 = 1 Left part of the equation: (11 * 7) mod 4 = 77 mod 4 = 1 Let's have a look at the same example (A = 11, B = 7, C = 4) – can you find the result of 77 mod 4 on the spot? 11 mod 4 and 7 mod 4 are easier to calculate: Such an equation may be useful when dealing with big numbers, and we don't know the modulo of that large number instantly. (A * B) mod C = (A mod C * B mod C) mod C Right part of the equation: (11 mod 4 + 7 mod 4) mod 4 = (3 + 3) mod 4 = 6 mod 4 = 2Īnalogically, the calculations are the same for subtraction. Left part of the equation: (11 + 7) mod 4 = 18 mod 4 = 2 The first stage is made to get rid of the quotient part, and then the mod operation is used again. So, the modulo of the sum of two numbers is equal to the sum of the modulo of those numbers calculated separately, then multiplied by the modulo divisor. (A - B) mod C = (A mod C - B mod C) mod C (A + B) mod C = (A mod C + B mod C) mod C We can also perform calculations on modulo operations. A = B + K * C where K is a some integer.Let's sum up what we've learned about different representations of modulo operations – all those statements below are equivalents: Modular arithmetic is, generally speaking, an arithmetic system for integers, where numbers "wrap around" a certain number.

#How do you do division in modular arithmetic how to

If the modulo definition doesn't appeal to you, and you're still unsure how to calculate modulo, have a look at the next paragraph, and everything should become crystal clear. Otherwise, the number r is the remainder of the division, where x is the dividend, and y is the divisor. Is true if such an integer q (called quotient) exists, then: y * q + r = x. In mathematics, there are many types of more elaborate modulo operations that require more thought.

Modulo operations in the case of the clock are so intuitive we don't even notice them. You just calculated you will wake up at 7 am 🕖.

To find the correct answer, you need to perform a modulo operation (mod 12) – you add these two numbers, and keep subtracting 12 until you get a number lower than 12. You can't just add 8 to 11, as there is no such time as 19 am. You wonder what the time will be when you wake up after 8 hours of sleep. Let's say it is late at night – 11 pm 🕚.