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I'm here today to teach you how to have fun with Redstone, now if you don't, you may just jump into a Minecraft sand well and drown.
Okay, first thing is first, the BASICS. You may already know that there are what we call 'Logic Gates' in all forms of machines from a computer to a simple on and off switch. We are going to be talking about the main logic gates for now. So let's get started.

The NOT Gate: The NOT Gate is what I think is the easiest logic gate to comprehend in Minecraft. It is basically an inverter. It inverts the input. For example, if I were to take an input of Redstone that is on, it would invert it and give an output of Redstone that is off.If it were off, it would be an output of on. This is one of the most used Redstone logic gates.

The OR Gate: The OR Gate is also VERY simple to understand, and is also called a Universal Logic Gate, this is because you can use this gate to make any other gate existent. OR basically means 'One input OR the other input  OR both will give us an output'. This is like saying 'Jeff's dog will get a treat if he jumps in the air OR he rolls over, OR does both'. This is also easy to comprehend.
(The NOR Gate is the same as the OR Gate except its output is inverted)

The AND Gate: The AND Gate reciprocates the OR gate except for one major difference. Instead of 'If one OR the other is on the output is on', it is 'If one AND the other are on the output is on, otherwise it is off'. So what this is saying is that you need to have BOTH inputs on in order to have the output on. This is like saying 'Jeff needs to turn the handle AND push the door to open it'.
(The NAND Gate is the same as an AND Gate except its output is inverted, the NAND Gate is also a universal gate)

The XOR Gate: The XOR Gate is also very similar to the OR gate but instead of 'One or the other or both', it is 'One or the other'. XOR means 'Exclusive OR', meaning only one of the inputs can be on or else I wont turn on. This is very important when dealing with Redstone calculators or ALUs. It is one of the main functions of a Redstone Adder or Subtractor.
(The XNOR Gate is the same as an XOR Gate but its output is inverted)

Those are all of the main basic logic gates I'm going to take you through today! These ones are the most important ones to be used and can help people a lot. There are PLENTY more to go through but that would be a bit much documentation for me to handle.

If you need any help or need some easy visuals, you can go to StephennJF's YouTube page, or you can also go to bennyscube's YouTube page for help too.
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Well, an administrator person said that it wouldn't count as an instructable so she said to post it as a forum. :p

You ought to post this as an instructable, but with your own visuals, not somebody else's.