Understanding Logic Gates

Inside your computer are billions of units called transistors. These transistors serve a variety of purposes, but commonly act as a type of very small light switch. Each switch can be turned on or off. Computer scientists often represent a switch being turned on by the number. one and a switch that turns off with the number zero these zeros and ones form a number system called binary and it is the fundamental language of computers from just these zeros and ones we end up with computers that can perform calculations create documents see images browse the web and more, how does that happen?

In this series we will explore the fundamentals of computer

logic

starting from the fundamentals and moving towards increasingly sophisticated systems using these switches our computers can store information each switch stores a single bit of information to 0 or a 1, but computers do not only store information, but rather they process it by transforming inputs into outputs, that is where

logic

gates

come in. Logic

gates

are the basic components of computer circuits. They accept inputs and produce outputs according to a set of logical rules. One of the simplest. Logic gates are the gate not represented graphically here. The gate does not take a single input, be it a 0 or a 1, and invert it so that the output is the opposite of whatever the input is.

If the input is a 1, then the gate does not generate a 0. if the input is 0, then the gate does not generate a 1 to represent the logical rule that this gate obeys, we can draw a truth table which is just a way of write the rules for some logical formula, this table says that if the input is 0 then the output is 1 and if the input is 1 the output is 0 often, although our computers need to be able to perform calculations not just with a single bit of information But with multiple bits of information, the y gate shown here, for example, is logical. gate that takes two inputs instead of one, let's call these two inputs a and B, as the name might suggest, the y gate will output a 1 when a and B are ones, but in all other cases y will output a 0, we can construct a TRUE. here also this truth table is a little bigger since with two inputs there are more possibilities to consider if a and B are 0 the output is 0 if a is 0 and B is 1 the output is 0 if a is 1 and B is 0 the output is still 0 and only when a and B are ones, the output is 1, meanwhile, the o gate is also a logic gate that takes two inputs, this gate generates a 1 when a is a 1 or when B is a 1 , then if both inputs are 0, the o gate outputs 0, but if either of the inputs is 1 or both inputs are 1, then the output of the o gate will also be 1, these logic gates alone follow fairly simple rules, but they can be combined with each other to form more complex calculations.

Imagine what would happen if, for example, we took two inputs, passed them to a NAND gate, and then passed that output to a non-gate. What would happen if both inputs were 0? The y gate will generate a 0 and the node will convert that 0 to 1 if only one of the inputs is 0, nothing changes, but if both inputs are 1, the y gate will generate a 1 and the node will convert that to a 0, otherwise words, this circuit. seems to do the opposite of what the and gate would do on its own, it turns out that inverting the result of an and calculation is such a common operation that it has its own logic gate, the NAND gate, this gate is equivalent to an and followed by a zero, then if the truth table and looks like this, then the NAND truth table is identical except that all the outputs are inverted when and when the output is 0 and it generates a 1 when and when I open a 1-man it generates a 0 as I could guess that if there is a logic gate to take the opposite of a NAND gate, there is also a logic gate that takes the opposite of an or gate, this is the nor gate when both inputs are zero or would normally output a zero, so so the nor gate would flip that and generate a 1 in all other cases at least one of the inputs is 1 so it would generate a 1 and the nor gate would generate a 0.

Instead, let's use these gates to solve a sample problem given two inputs a and B. We would like to calculate whether exactly one of them is 1. What does it mean logically that exactly one of these two inputs is 1? It means that A or B must be 1, but it also means that they can be 1. Both are a 1, so logically we could represent this as a or B and not as a and B to mean that one of the two must be a 1 but both cannot be a 1. We could also create a circuit to perform this calculation, but this circuit is starting to look quite complex, so once again there is a logic gate to solve this problem, precisely the exclusive or gate generates a 1 when exactly one of its inputs is a 1, so if only a is 1 or only B is 1, then the output of exclusive-o is 1, but otherwise, if both inputs have the same value, either both zeros or both ones, then the output is 0 and just for completeness, there is also a gate to invert the exclusive gate or the nor exclusive gate, this gate does the opposite of what exclusive or does while exclusive or will generate a one when the two inputs are different between yes exclusive nor will generate a one when the two inputs are equal both zeros or both ones these illogical gates are not manned nor exclusive or and exclusive nor form the basis of computation in computers combining only these few logic gates, each of which obeys a relatively simple logical rule, we can build computers that can represent all the data and perform all the complex calculations that our computers do every day.