Booyleen+Logic+and+Gates

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. Now computers do them with apparent ease. How can a "chip" made up of silicon and wires do something that seems like it requires human thought? 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**. Boolean logic, originally developed by George Boole in the mid 1800s, allows quite a few unexpected things to be mapped into bits and bytes. 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. In this article,we will first discuss simple logic "gates," and then see how to combine them into something useful.

=Simple Gates= There are three, five or seven simple gates that you need to learn about, depending on how you want to count them (you will see why in a moment). With these simple gates you can build combinations that will implement any digital component you can imagine. These gates are going to seem a little dry here, and incredibly simple, but we will see some interesting combinations in the following sections that will make them a lot more inspiring. If you have not done so already, reading [|How Bits and Bytes Work] would be helpful before proceeding. The simplest possible gate is called an "inverter," or a **NOT gate**. It takes one bit as input and produces as output its opposite. The table below shows a logic table for the NOT gate and the normal symbol for it in circuit diagrams:

|| You can see in this figure that 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). The table shows how the gate behaves. When you apply a 0 to A, Q produces a 1. When you apply a 1 to A, Q produces a 0. Simple. The **AND gate** performs a logical "and" operation on two inputs, A and B:
 * **NOT Gate**
 * **B** || **Q** ||  ||
 * 0 || 1 ||
 * 1 || 0 ||  ||   ||

|| 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. You read this table row by row, like this:
 * **AND Gate**
 * **A** || **B** || **Q** ||  ||
 * 0 || 0 || 0 ||
 * 0 || 1 || 0 ||
 * 1 || 0 || 0 ||
 * 1 || 1 || 1 ||  ||   ||
 * **AND Gate** ||
 * **A** || **B** || **Q** ||  ||   ||
 * 0 || 0 || 0 || //If A is 0 AND B is 0, Q is 0.// ||
 * 0 || 1 || 0 || //If A is 0 AND B is 1, Q is 0.// ||
 * 1 || 0 || 0 || //If A is 1 AND B is 0, Q is 0.// ||
 * 1 || 1 || 1 || //If A is 1 AND B is 1, Q is 1.// ||  ||

The next gate is an **OR gate**. Its basic idea is, "If A is 1 **OR** B is 1 (or both are 1), then Q is 1."

|| Those are the three basic gates (that's one way to count them). It is quite common to recognize two others as well: the **NAND** and the **NOR** gate. These two gates are simply combinations of an AND or an OR gate with a NOT gate. If you include these two gates, then the count rises to five. Here's the basic operation of NAND and NOR gates -- you can see they are simply inversions of AND and OR gates:
 * **OR Gate**
 * **A** || **B** || **Q** ||
 * 0 || 0 || 0 ||
 * 0 || 1 || 1 ||
 * 1 || 0 || 1 ||
 * 1 || 1 || 1 ||  ||   ||

|| 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 are their tables:
 * **NOR Gat**[[image:http://static.howstuffworks.com/gif/bool-nor.gif align="center"]]**e** ||
 * **A** || **B** || **Q** ||
 * 0 || 0 || 1 ||
 * 0 || 1 || 0 ||
 * 1 || 0 || 0 ||
 * 1 || 1 || 0 ||  ||   ||
 * **NAND Gate**
 * **A** || **B** || **Q** ||
 * 0 || 0 || 1 ||
 * 0 || 1 || 1 ||
 * 1 || 0 || 1 ||
 * 1 || 1 || 0 ||  ||   ||

|| || 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. Here is one implementation:
 * **XOR Gate**
 * **A** || **B** || **Q** ||
 * 0 || 0 || 0 ||
 * 0 || 1 || 1 ||
 * 1 || 0 || 1 ||
 * 1 || 1 || 0 ||  ||   ||
 * **XNOR Gate**
 * **A** || **B** || **Q** ||
 * 0 || 0 || 1 ||
 * 0 || 1 || 0 ||
 * 1 || 0 || 0 ||
 * 1 || 1 || 1 ||  ||   ||

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. Since there is a well-understood symbol for XOR gates, it is generally easier to think of XOR as a "standard gate" and use it in the same way as AND and OR in circuit diagrams.