# Modulo arithmetic

In programming, taking the modulo is how you can fit items into a hash table: Play the mod N mini-game!

For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation: This optimization is not possible for languages in which the result of the modulo operation has the sign of the dividend including Cunless the dividend is of an unsigned integer type.

Add them up and divide by 4 — whoever gets the remainder exactly goes first. Picking A Random Item I use the modulo in real life. Putting Items In Random Groups Suppose you have people who bought movie tickets, with a confirmation number. One correct alternative is to test that it is not 0 because remainder 0 is the same regardless of the signs: For all congruent numbers 2 and 14adding and subtracting has the same result.

This is a bit more involved than a plain modulo operator, but the principle is the same. Where will the hour hand be in 7 hours? They are congruent, indicated by a triple-equals sign: We have 4 people playing a game and need to pick someone to go first.

For the mod m notation, see congruence relation. We can just add 5 to the 2 remainder that both have, and they advance the same. Odd, Even and Threeven Shortly after discovering whole numbers 1, 2, 3, 4, 5… we realized they fall into two groups: As your hash table grows in size, you can recompute the modulo for the keys.

This is huge — it lets us explore math at a deeper level and find relationships between types of numbers, not specific ones. Thus, the sign of the remainder is chosen to be nearest to zero. For example, to test if an integer is odd, one might be inclined to test if the remainder by 2 is equal to 1: Some calculators have a mod function button, and many programming languages have a similar function, expressed as mod a, nfor example.

What about the number 3? You have a flight arriving at 3pm. Well, they change to the same amount on the clock! Uses Of Modular Arithmetic Now the fun part — why is modular arithmetic useful? Despite its widespread use, truncated division is shown to be inferior to the other definitions.

Give people numbers 0, 1, 2, and 3. See the above link for more rigorous proofs — these are my intuitive pencil lines. For example, we can make rules like this: This may be useful in cryptography proofs, such as the Diffie—Hellman key exchange. What time will it land? So it must be 2. What do you do?Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity, which is known as the modulus (which would be 12 in the case of hours on a clock, or 60 in the case of minutes or seconds on a clock).

Formally, modular. The same is true in any other modulus (modular arithmetic system). In modulo, we count. We can also count backwards in modulo 5. Any time we subtract 1 from 0, we get 4. So, the integers from to, when written in modulo 5, are where is the same as in modulo 5.

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus). Given two positive numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n.

Read and learn for free about the following article: What is modular arithmetic? If you're seeing this message, it means we're having trouble loading external resources on our website.

We would say this as A A A A modulo B B B B is equal to R R R R. Where B B B B is referred to as the modulus. For example. A reader recently suggested I write about modular arithmetic (aka “taking the remainder”). I hadn’t given it much thought, but realized the modulo is extremely powerful: it should be in our mental toolbox next to addition and multiplication.

Instead of. An introduction to the notation and uses of modular arithmetic. The best way to introduce modular arithmetic is to think of the face of a clock.

Modulo arithmetic
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