Good Essay About Digital Electronics

DeMorgan’s Theorem is one of the most important transformation rules in digital electronics. It is a pair of transformation rules which could be applied in propositional logic and are both valid for rules of inference. It was named after its developer Augustus De Morgan who is a British Mathematician. The simplest way to define DeMorgan’s Theorem is that the logical expressions remains unchanged when the inversion bar of the expression is broken and the operation is changed to its opposite.
DeMorgan’s Theorem come about in order to simplify logical expressions in mathematics. It was influenced by the algebraization of logic or creation of logical expressions by George Boole. It could be implemented in basic gates used in digital electronics. It is also used in reducing the complexity of digital logic circuits. For example in electronics, a NAND gate could be changed into an inversion followed by an OR gate.
Karnaugh Maps of simply K-maps is a specialized form of truth table in which it simplifies Boolean algebra expressions. Some of its advantages include efficiency. K-maps are used in order to reduce the required logic of the problem expressions. It is easy to visualize in small number of variable maps. The K-map is also advantageous in reducing the number of basic gates for solving logic expressions. Since it reduces the basic gates, it also reduces the possible errors.
However, K-maps are not easy to visualize in maps with large number of variables. The equations could not be easily acquired with more than 5 variables with a K-map. Although it does not fail on large quantity of variables, it is better to use truth table instead of K-maps due to the difficulty in visual aid. For people who are slow in analyzing Boolean expressions, K-maps are also not advisable to use since it could result into slower simplifications.
One of the best ways to reduce the number of Boolean expressions is using the K-maps. This is because the focus of the simplifications of Boolean expressions is by reducing the number of logic gates instead of variables. However, in the minimization of the Boolean expressions, the algorithms or methods do not usually focus on the number of characters or variables. The algebraic expressions could be difficult to acquire when using K-maps since it is only visually easy when there are few variables.
The most efficient approach in simplifying Boolean expression is to use algorithm which has an identical functionality with the K-maps. One of these algorithms or method is the Quine-McCluskey algorithm. For example, Quine-McCluskey algorithm is a method of simplifying Boolean expressions which uses tabular form and is more efficient than K-maps since it could handle large number of variables. The method of Quine-McCluskey algorithm has two major steps. First is the identification of all prime implicants in the function. Second is the usage of these prime implicants in a chart in identifying the essential prime implicants.
One of the main advantages of Quine-McCluskey algorithm is that it could be easy to use for large quantity of variables unlike the K-Map method. It is a method of simplification of Boolean expressions which could be applied to any quantity of variables. However, the simplification process of Quine-McCluskey algorithm could be very lengthy and time consuming. Since it could process large quantity of variables, it could provide difficulties for users since it should follow the basic steps of Quine-McCluskey algorithm.
However, the Quine-McCluskey algorithm is algebraic in nature. It means it could be easily programmed into a computer in order to reduce the time for it to apply. It could easily identify prime implicants as well as implicate on any function with the use of computers.