Logicworks simple circuit5/17/2023 ![]() ![]() ![]() If you try all four different patterns for A and B and trace them through the circuit, you will find that Q behaves like an XOR gate. The idea behind an XOR gate is, "If either A OR B is 1, but NOT both, Q is 1." The reason why XOR might not be included in a list of gates is because you can implement it easily using the original three gates listed. The final two gates that are sometimes added to the list are the XOR and XNOR gates, also known as "exclusive or" and "exclusive nor" gates, respectively. Here's the basic operation of NAND and NOR gates - you can see they are simply inversions of AND and OR gates: NOR Gate A B Q If you include these two gates, then the count rises to five. These two gates are simply combinations of an AND or an OR gate with a NOT gate. It is quite common to recognize two others as well: the NAND and the NOR gate. Those are the three basic gates (that's one way to count them). Its basic idea is, "If A is 1 OR B is 1 (or both are 1), then Q is 1." A B Q You read this table row by row, like this: A B Qġ 1 1 If A is 1 AND B is 1, Q is 1. The idea behind an AND gate is, "If A AND B are both 1, then Q should be 1." You can see that behavior in the logic table for the gate. The AND gate performs a logical "and" operation on two inputs, A and B: A B Q The NOT gate has one input called A and one output called Q ("Q" is used for the output because if you used "O," you would easily confuse it with zero). In this article,we will first discuss simple logic "gates," and then see how to combine them into something useful. The great thing about Boolean logic is that, once you get the hang of things, Boolean logic (or at least the parts you need in order to understand the operations of computers) is outrageously simple. Boolean logic, originally developed by George Boole in the mid 1800s, allows quite a few unexpected things to be mapped into bits and bytes. If you want to understand the answer to this question down at the very core, the first thing you need to understand is something called Boolean logic. How can a "chip" made up of silicon and wires do something that seems like it requires human thought? Now computers do them with apparent ease. ![]() Have you ever wondered how a computer can do something like balance a check book, or play chess, or spell-check a document? These are things that, just a few decades ago, only humans could do. Boolean logic affects how computers operate. ![]()
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