What are logic gates?
In our real world, there are extremely complex electronic devices with
complicated functions, such as computers and smartphones, which contain very
complex electronic components called processors, as well as memory. However,
if we look more closely at these complex circuits, we will find that they
are made up of simple electronic circuits with simple and easy-to-understand
logical functions called logic gates. Logic gates are the cornerstone of
building digital electronic circuits. The internal structure of logic gates
is made up of a large number of transistors. Logic gates are electronic
circuits that have multiple inputs and a single output, and they perform
simple logical functions that we will study in this article.
There are three basic logic gates, and we explained them in detail in the
previous article. You can refer to them via the link:
the basic logic gates: NOT, AND, OR
The NOR logic gate
In total, there are seven logic gates, three of which are fundamental and were
explained in the previous article. The other four logic gates are actually
combinations of two or more fundamental logic gates.
The "NOR" logic gate is a gate composed of two fundamental gates, "NOT" and
"OR," which perform their functions simultaneously, thus providing a new
logical function.
The logical function of the NOR logic gate
The NOR logic gate gives a logic state 1 at the output if all the inputs are at logic state 0.
Truth table of the NOR logic gate
We can express the function of the "NOR" logic gate in the form of a truth table, which gives us all the output values for all possible combinations of input states.
Algebraic equation of the NOR logic gate
The function of a logic gate contains two logical operations: "OR," which we express with the symbol +, and the inverter, which we denote by a bar over the name of the input.
Symbol of the NOR logic gate
The NOR logic gate with multiple inputs
The "NOR" logic gate is available with multiple inputs as needed, and it is possible to combine several logic gates to increase the number of inputs if necessary.
The NAND logic gate
The "NAND" logic gate performs the function of an "AND" gate followed by a "NOT" gate, as it is fundamentally composed of the two basic gates "AND" and "NOT." Its logical function is as follows: the "NAND" logic gate outputs logic state 0 in only one case, namely when all the inputs are at logic state 1.
Truth table of the NAND logic gate
Symbol of the NAND logic gate
Algebraic expression of the NAND logic gate
We express the "NAND" function in the algebraic expression using a dot that represents multiplication in mathematics and a bar above the names of the inputs that represents the inverter.
NAND logic gate with multiple inputs
The XOR logic gate
The function of the XOR logic gate is that if its inputs contain different logic values, it gives a logic state 1 at the output. Conversely, if the inputs have the same logic state, then the output will be logic state 0.
Symbol of the XOR logic gate
Truth table of the XOR logic gate
Algebraic expression of the XOR logic gate
In the algebraic expression, we represent the function of the XOR logic gate by the symbol + inside a circle (⨁).
The function of the XOR logic gate can be expressed using the basic logic gates "OR," "NOT," and "AND" by the following equivalent expression:
The XNOR logic gate
LThe "XNOR" logic gate is a combination of the "XOR" gate and the "NOT" logic gate. Its logical function is that it gives a logic state 1 at the output if all the inputs have identical logic states.
Symbol of the XNOR logic gate
Truth table of the XNOR logic gate
Algebraic expression of the XNOR logic gate
Since the "XNOR" logic gate is the inverse of the "XOR" logic gate, the algebraic expression of the "XNOR" gate is the same as that of the "XOR" gate, with a bar placed above the equation to indicate inversion. This can be represented as follows:
There is an equivalent logical expression for the "XNOR" logic gate using the basic logic gates, and the expression is as follows:
Post a Comment