Binary operations math is fun

Shortly after discovering whole numbers 1, 2, 3, 4, 5… we realized they fall into two groups:. This is huge — it lets us explore math at a deeper level and find relationships between types of numbers, not specific ones. For example, we can make rules like this:. These rules are general — they work at the property level. What about the number 3?

Where will the hour hand be in 7 hours? So it must be 2. We do this reasoning intuitively, and in math terms:.

They are congruent , indicated by a triple-equals sign: So, the clock will end up 1 hour ahead, at 9: Well, they change to the same amount on the clock! We can just add 5 to the 2 remainder that both have, and they advance the same. For all congruent numbers 2 and 14 , adding and subtracting has the same result.

We ignore the overflow anyway. See the above link for more rigorous proofs — these are my intuitive pencil lines. You have a flight arriving at 3pm. What time will it land?

Suppose you have people who bought movie tickets, with a confirmation number. You want to divide them into 2 groups. What do you do? Divide by 3 and take the remainder aka mod 3. In programming, taking the modulo is how you can fit items into a hash table: As your hash table grows in size, you can recompute the modulo for the keys.

I use the modulo in real life. We have 4 people playing a game and need to pick someone to go first. Play the mod N mini-game! Give people numbers 0, 1, 2, and 3.

Add them up and divide by 4 — whoever gets the remainder exactly goes first. Oh, you need task C1 which runs 1x per hour, but not the same time as task C? The neat thing is that the hits can overlap independently.

Similarly, when programming you can print every th log item by doing: What can you deduce quickly? So we can use modulo to figure out whether numbers are consistent, without knowing what they are! A contradication, good fellows!

The modular properties apply to integers, so what we can say is that b cannot be an integer. Playing with numbers has very important uses in cryptography.

Geeks love to use technical words in regular contexts.

In addition to public-key cryptography like Diffie Hellman and RSA, modular operations are very useful in private-key symmetric-key algorithms like the Advanced Encryption Standard AES. Modular operations are useful there because you can represent a byte as a polynomial with coefficients that are either 1 or 0. Once you do this, you can take advantage of a lot of nice mathematical properties. Instead of dividing by a number, you can divide by a polynomial and things just work out. Logarithms work in a similar way.

I had fun learning about the details and wrote about the details in Act 3 of my stick figure guide to AES. It only works this way if both numbers are positive. This is confusing enough, but the modulo operator in programming languages has behavior that is hard to predict for negative values. Notice that that article also states, incorrectly, that modulo is the same as remainder. The a is the number of steps you take, with negative being backwards.

Whenever a multiplication has at least one dominant allele, the result is even.

abstract algebra - Fun problems with binary operations. - Mathematics Stack Exchange

Only when both multiplicands are odd, is the result odd. Threeven, Modulo, Clock Math, and Cryptography. This entry was posted in! Jess, I think I can answer your question. What number is this? Find the last digit of 3 to the power of First we make a chart:. It divides in evenly so 1 the fourth number in the pattern is the last digit of 3 to the power of Good article, there is just a small mistake: Thank you very very much: I recently saw the following video: In which at 4min and 35seconds, following math-e-magic happens: Menu Home Articles Calculus Guide Contact About Newsletter Blog Feedback.

Calculus, Better Explained is now an Amazon bestseller. Grab your copy and learn Calculus intuition-first! Fun With Modular Arithmetic. Contents Odd, Even and Threeven Enter the Modulo Clock Math Fun Property: Math just works Uses Of Modular Arithmetic Onward and Upward Other Posts In This Series. You can choose reporting category and send message to website administrator. Admins may or may not choose to remove the comment or block the author.

Binary Numbers - Computer Science Unplugged

And please don't worry, your report will be anonymous. Making Your Math Simple Part II - Multiplication With 11 in Just 5 Seconds. When Teaching, Multiplication Just Doesn't Add Up.

Can anyone answer this question and explain it? In mod 6, What is 3 divided by 5?? Fun With Modular Arithmetic Eli Foner.

What is binary? - Definition from umypecodayok.web.fc2.com

This article explains everything really clearly and I totally understand mods now!!!! First we make a chart: Is there a good book you could recommend for starting out with modular arithmetic? Hi, I recently saw the following video: Thank you for your time!

Mixed Operations Math Worksheets

Load Rest of Comments. In This Series Techniques for Adding the Numbers 1 to Rethinking Arithmetic: A Visual Guide Surprising Patterns in the Square Numbers 1, 4, 9, 16… Fun With Modular Arithmetic Learning How to Count Avoiding The Fencepost Problem A Quirky Introduction To Number Systems Another Look at Prime Numbers.

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