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Introduction to Logic Gates

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Introduction to Logic Gates Introduction to Logic Gates Introduction Logic gates are used when designing logical circuits for machines. Logic gates usually take in two inputs, which can be represented with 1 and 0, true and false, or on and off. While two inputs are traditional, some diagrams will draw gates with multiple inputs to save space. In reality this would be done with multiple copies of the gate. Logic gates always have a single output give in the same format as their inputs. Logic gates can be broken down into three categories: basic gates, negative gates, and exclusive gates. Logic gates are used to perform various calculations and run through computations. They may seem simple but when used together they can create things like calculators and computer memory. Each logic gate has a visual representation, and using these representations, larger scale diagrams can be made. The most common application of logic gates is probably in Minecraft, which is the main reason the game is encouraged to begin an interest in computer programming. Minecraft uses things called Redstone to make wires, and the gates do not exist themselves, but are actually made from just wires and an on switch. Basic Gates There are two main basic gates, the AND gate and the OR gate. These two gates, along with NOT gates which will be explained later, can make any other gate explained in this guide. AND Gate The AND gate takes two inputs and returns true when both inputs are true. The primary use of this gate is to make sure multiple conditions are met. In essence, if this gate were a door, it would not open unless you have all required keys. AND can be represented textually with the symbol ˄ The AND gate’s diagram and output is shown below: A B Q 0 0 0 0 1 0 1 0 0 1 1 1 OR Gate The OR gate takes two inputs and returns true when an input is true. The primary use of this gate is to make sure you meet at least one requirement. In essence, if this gate were a door, any of its keys would open it. OR can be represented textually with the symbol ˅ The OR gate’s diagram and output is shown below: A B Q 0 0 0 0 1 1 1 0 1 1 1 1 Negative Gates All negative gates follow the basic idea of a not gate, which is “reverse the output.” There are four gates that fall under the category of negative gates, the NOT, NAND, NOR, and NXOR. We will discuss XNOR with exclusive gates, since we’ve yet to discuss XOR. When drawing diagrams for negative gates, a circle is used to indicate the negation. NOT Gate The NOT gate is the only gate to not follow the two input one output rule. This gate takes one input and then reverses it. NOT can be represented textually in a multitude of ways, ~A, A’ and 퐴̅ are all valid, The NOT gate’s diagram and output is shown below: A OUT 0 1 1 0 NAND Gate The NAND gate is the inverse of the AND gate. It is simply comprised of an AND gate with a NOT gate at the end, however it is easier and faster to represent it as its own entity. This gate works very similarly to the AND gate, however it is used to make sure that at least one of multiple conditions is not met. NAND would be represented textually as ~(A ˄ B) The NAND gate’s diagram and output is shown below: A B Q 0 0 1 0 1 1 1 0 1 1 1 0 NOR Gate The NOR gate is the inverse of the OR gate. As one would predict, it is made by placing a NOT gate at the end of an OR gate. This gate works similarly to the OR gate, however this gate makes sure absolutely none of the conditions are met. NOR would be represented textually as ~(A ˅ B) The NOR gate’s diagram and output is shown below: A B Q 0 0 1 0 1 0 1 0 0 1 1 0 De Morgan’s Law: While not a gate, there is an interesting rule observed by De Morgan when utilizing negation. You may have noticed that the tables for NAND and NOR looked familiar. This is because, according to De Morgan’s Law, A NAND B, ~(A ˄ B), is equal to (NOT A) OR (NOT B), ~A ˅ ~B and A NOR B, ~(A ˅ B) is equal to (NOT A) AND (NOT B), ~A ˄ ~B. This can be shown with the following table: A B ~A ~B ~(A ˄ B) ~A ˅ ~B ~(A ˅ B) ~A ˄ ~B 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 Exclusive Gates Exclusive is an adjective that can be applied to the OR and NOR gates to make XOR and XNOR. Exclusive or works more like the English definition of or. With computers, OR says “Is this or that true?” and responds with “yes” if at least one is true. XOR, on the other hand asks “Is only this or only that true?” XOR Gate This means that the XOR gate returns true when only one input is true. An easy way to think about this would be as a light switch. If there are two light switches, and one is in the on position, the light should be on. However if you flip the switch for the other light switch, you still expect the light to turn off. An XOR gate makes that happen. There is no simple textual representation for an XOR gate. This is because, as mentioned earlier, it can be made using AND, OR, and NOT gates. One such example is (~A ˄ B) ˅ (A ˄ ~B) The XOR gate’s diagram and output is shown below: A B A XOR B 0 0 0 0 1 1 1 0 1 1 1 0 NXOR Gate The XNOR gate, while seeming like an odd concept, is actually very useful in circuits. Since the XOR gate return true when the inputs are different, one true and one false, the XNOR gate returns true when the inputs match. This means that XNOR is unique in that it does not matter whether the input is true or false, so long as both inputs match. There is no simple textual representation for an XNOR gate. This is because, as mentioned earlier, it can be made using AND, OR, and NOT gates. One such example is (A ˄ B) ˅ (~A ˄ ~B) The XOR gate’s diagram and output is shown below: A B A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1 Conclusion Logic gates are fairly simple concepts to grasp, and can be used to make complex designs such as locks, multiplexors, toggles, and much more. These complex designs can in turn be used to make larger and larger projects. While there are certain gates that have designs for simplicity’s sake, they all can be made out of the three basic gates. All of the diagrams used were taken from Wikipedia. .
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