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Binary and non-binary are two terms that might really scare you, much like an operation may scare you. But don't worry, this lesson is super fun and super easy. You'll learn the definitions of these terms and see examples of each.

Mathematical Operations

This lesson has nothing to do with surgery, although it has everything to do with two different operations. Mathematical operations of course. They are the binary and non-binary operations and unlike brain surgery, this lesson's operations aren't all that difficult to understand nor master. So, don't get a headache before we even begin here. This lesson will define and show you what a binary and non-binary operation is in math.

Binary and Non-Binary Operations

First, let's just simply define what a mathematical operation is. An operation is a mathematical process. Yep, that's the definition and it refers to processes like the ones you are really familiar with, such as addition, subtraction, multiplication and division. Next, let's define binary. Binary implies something that is made up of or indicates two, since 'bi' is a prefix that means two. Like a bicycle has two wheels.

Logically, if we put our definitions together, this means a binary operation is a mathematical process that uses two numbers to accomplish something. On the other hand, a non-binary operation is a mathematical process that only needs one number to accomplish something.

Examples of Binary Operations

Okay, with that really simple stuff out of the way, we're going to move on to some even simpler and funner stuff. Not sure if funner is a word, but, it is now. Not long ago, my Mom lent me $100. I gave my Mom $20 and then, another $80 a few days after that to pay her back. This means, I repaid her in full since $20 + $80 = $100. Addition is a type of binary operation since I used two different numbers ($20 and $80) to come up with my answer.

Outside my room now, I see a squirrel digging into the ground to find an acorn; the hole contains three acorns. The squirrel takes one acorn out; how many acorns are left in the hole? 3-1 = 2. Subtraction is a kind of binary operation since we clearly used two numbers to perform this operation. The numbers 3 and 1 that is.

Earlier this week, I went to a restaurant where I was trying to find out how much I should tip. I decided that the $10 meal deserved a 20% tip; so, to figure out how much I should tip in dollars, I multiplied $10 x 0.2 to come up with the answer of $2. Multiplication is another binary operation since I used $10 and 0.2 as my two numbers to accomplish this operation.

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Later that same day, a few friends came over to my place and I cooked some of my famous grub. I had three friends over; on the stove, I had to split the entire meal into four different portions so we each had something to eat. This meant that I had to divide one whole pan full of food into 4 parts. ¼ = 0.25. Everyone got 25% of the food. Division is another example of a binary operation.

Examples of Non-Binary Operations

Okay, so now you've got binary operations down pat. Let's move on to examples of non-binary operations. Recall that these are operations where an answer can be figured out by using only one number as the input. Some great examples of this include:

Square roots

The square root of 4 is 2. This operation was performed on just one number (4) in order to figure out our answer.

Factorials

A factorial is that famous operation denoted as n! Where the factorial is denoted by the exclamation mark. For example, 3! = 3x2x1 = 6 Again, this is a non-binary operation because to get our answer of 6, we originally began with just one input- that of 3.

And finally, another example is:

Absolute values

The absolute value is the value of a number without a sign. So for example, the absolute value of -6, written as negative six in between two vertical lines, is equal to 6. The absolute value of 10, written as 10 in between two vertical lines, is equal to 10. Again, the mathematical process used here relies solely on one number and thus is an example of a non-binary operation.

Lesson Summary

See, I told you this lesson on operations wasn't brain surgery! An operation is a mathematical process since binary implies something that is made up of or indicates two, then a binary operation is a mathematical process that uses two numbers to accomplish something. On the flip side, a non-binary operation is a mathematical process that only needs one number to accomplish something.

Examples of binary operations include addition, subtraction, multiplication, and division. Examples of non-binary operations include square roots, factorials, and absolute values.

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