LOGIC GATESBorlagdan, Jhon Errol L.Dela Torre, Adrian C.Militar, Ryan B.Palaca, Jaysam S.Advincula, John Dale B.Alim, Christian Paul F.Daang, David F.

Digital Logic GatesIn electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more logical inputs, and produces a single logical output. Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.In the following examples, each logic gate except the NOT gate has two inputs, A and B, which can either be 1 (True) or 0 (False). The resulting output is a single value of 1 if the result is true or 0 if the result is false. OR - True if either A or B are True NOR - OR followed by NOT: True only if A and B are both False AND - True if A and B are both True NAND - AND followed by NOT: False only if A and B are both True NOT - Inverts value: True if input is False; False if input is True XOR - True if either A or B are True, but False if both are True XNOR - XOR followed by NOT: True if A and B are both True or both False

Logic Gate SymbolsOR The OR gate gets its name from the fact that it behaves after the fashion of the logical inclusive "or." The output is "true" if either or both of the inputs are "true." If both inputs are "false," then the output is "false."

NOR

The NOR gate is a combination OR gate followed by an inverter. Its output is "true" if both inputs are "false." Otherwise, the output is "false."

AND

The AND gate is so named because, if 0 is called "false" and 1 is called "true," the gate acts in the same way as the logical "and" operator.

NAND

The NAND gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation "and" followed by negation. The output is "false" if both inputs are "true." Otherwise, the output is "true."

NOT

A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. It reverses the logic state.

XOR

The XOR (exclusive-OR) gate acts in the same way as the logical "either/or." The output is "true" if either, but not both, of the inputs are "true." The output is "false" if both inputs are "false" or if both inputs are "true."

XNOR

The XNOR (exclusive-NOR) gate is a combination XOR gate followed by an inverter. Its output is "true" if the inputs are the same and "false" if the inputs are different.

Combinational LogicThe term "combinational" comes to us from mathematics. In mathematics a combination is an unordered set, which is a formal way to say that nobody cares which order the items came in. Most games work this way, if you rolled dice one at a time and get a 2 followed by a 3 it is the same as if you had rolled a 3 followed by a 2. With combinational logic, the circuit produces the same output regardless of the order the inputs are changed.There are circuits which depend on the when the inputs change, these circuits are called sequential logic. Even though you will not find the term "sequential logic" in the chapter titles, the next several chapters will discuss sequential logic.Practical circuits will have a mix of combinational and sequential logic, with sequential logic making sure everything happens in order and combinational logic performing functions like arithmetic, logic, or conversion.You have already used combinational circuits. Each logic gate discussed previously is a combinational logic function. Let's follow how two NAND gate works if we provide them inputs in different orders.

We begin with both inputs being 0.

We then set one input high.

We then set the other input high.

So NAND gates do not care about the order of the inputs, and you will find the same true of all the other gates covered up to this point (AND, XOR, OR, NOR, XNOR, and NOT).