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Logic gates are in every IC and microchip today, they practically control modern electronics.Personally I like to stick with capacitors and resistors and simple stuff like that but thanks to instructables user rtty21 I learned how to make a NOR gate and now I have countless ideas of what to with them, so here I will discuss some uses of different gates and how to make them. You should at least have a basic knowledge of logic gates to understand this. 

A/B=input(s)
Q=output
1=high
0=low

-=sorry about some of the messed up pictures, I'm trying to get it resolved=-

Step 1: NOT Gate

This is perhaps the most simple gate, it has one input and one output. It is known as an inverter because its output is opposite to its input. A representing the input, Q representing the output: Q=NOT A (thus the name "NOT"). There is an IC that uses six NOT gates called a 4049 CMOS hex inverter buffer. 

A  | Q
 1 | 0
 0 | 1

Step 2: AND Gate

The AND gate only has a "true" output of both of its inputs are "true". This means thats will only be high if both the inputs are high, if one is high and one low the output will be low. So Q=A & B (thus the name AND gate). 

 A | B | Q 
 0 | 0 | 0
 1 | 0 | 0
 0 | 1 | 0
 1 | 1 | 1 

Step 3: NAND Gate

The NAND gate is the opposite of an AND gate, the name stands for "NOT AND". One of the inputs have to be low to get a high, two highs is a low. The 4011 CMOS IC uses four NAND gates. The NAND gate can be used to make any other gate and it's possible to make a computer of NAND gates alone. Q = (NOT) A AND B (thus the name NAND).

 A | B | Q
 0 | 0 | 1
 0 | 1 | 1
 1 | 0 | 1
 1 | 1 | 0

Step 4: OR Gate

The OR gate uses the high input as the high output, the output is always high unless the inputs are both low. Four OR gates are used in the 4071 CMOS IC. Q=A or B (thus the name OR gate) 

 A | B | Q 
 0 | 0 | 0
 0 | 1 | 1
 1 | 0 | 1
 1 | 1 | 1

Step 5: NOR Gate

The NOR gate is perhaps the most useful gate of all. It's the opposite of an OR gate, the name means "NOT OR". Like the NAND gate this gate can also be used to make any other gate. Q=(NOT) A or B (thus the name NOR gate). I will make an extra step for all of the uses of the NOR and NAND gates because theres so many.

 A | B | Q
 0 | 0 | 1
 0 | 1 | 0
 1 | 0 | 0
 1 | 1 | 0

Step 6: EX-OR Gate

The name of the XOR gate means exclusive OR. There isn't much to say about this except that the out put is high only if the inputs are high and low.  Q = (A AND NOT B) OR (B AND NOT A).

 A | B | Q
 0 | 0 | 0
 0 | 1 | 1
 1 | 0 | 1
 1 | 1 | 0

Step 7: EX-NOR Gate

The name of the EX-NOR gate comes from  exclusive NOR. This gate is opposite or the EX-OR so the output will only be high if both inputs are high/low. Q = (A AND B) OR (NOT A AND NOT B) I do not have a schematic for this one, I would appreciate it if any one could provide one. 

A | B | Q
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1

Step 8: Uses of the NOR and NAND Gates

Because both of these gates can be used to make any other gate I decided to make another step for it. All or the pictures will be in pares of two, the first is the desired gate, the second is the equivalent in NAND or NOR gates. Although NAND and NOR gates are opposite they are both equivalent in this step so it doesn't matter which one you use.
<p>hi! i'm wondering how is this gonna differ to a three input xor using mosfet?</p>
The XNOR (and all other logic gate chips I've ever seen) has its own voltage and ground inputs that the user supplies. This voltage source is independent of the inputs for each gate on the chip. So the power is always available and the internal circuitry determines if the gate inputs will allow current to flow through to the outputs.
Thanks, I now understand a lot better. However, I don't understand one thing. Let's say we're using the XNOR gate. If A=0 and B=0 then Q=1. How? Where does Q get power from if A and B are low?
Thank you for making this<br>
Your welcome, sorry about some of the pictures.
im bored<br>
cuz ur fat
obama<br>
ithinknot

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