Boolean algebra plays an important role in mathematics and other well renowned fields of science such as physics and computer science etc. Boolean algebra is known by another name called logic gates. It was introduced by Gorge Boole in 19th of century.
Boolean Algebra is a very useful tool that helps the user according to their needs and also explains the logic of statement or functions etc. In short, it’s a powerful mathematical tool that had a major impact on the modern world.
The concept of the logic gate brings us further advances in Artificial intelligence, Data Science, Cybersecurity and many other technological fields.
Boolean Algebra
Boolean algebra is a branch of mathematics that focuses on operations and variables within binary systems. It primarily deals with binary values often represented as true/false, yes/no, or 0/1. This form of algebra underpins the functioning of logic gates, which are fundamental in digital circuits and computer science.
Boolean algebra applies these binary values in various logical operations and propositions, forming the basis for much of modern computing and digital electronics. It is widely utilized in areas ranging from computer programming to electrical engineering, playing a crucial role in the development and functioning of digital systems.
Types of logic gates and their symbols
There are three types of logical gates and other then these gates are formed by the combination these gates. So, the logical gates are as follows:
- AND gate (*)
- OR gate (+)
- NOT gate (!)
These gates are also known as operators. Like, And operator, Or operator and Not operator. Let us take a concept of these gates that how it works. In mathematics, Boolean algebra is known as the part of algebra it is widely used in statistics and set theory.
AND gate:
The AND gate is a fundamental digital logic gate that has two or more inputs in the form of preposition and only have one output. The output of and gate is ‘1’ and ‘true’ only when both the output would be ‘1’ and ‘true’.
In the truth table ‘0’ represents the ‘false’ and ‘1’ represents the ‘true’. AND gate implements the Boolean function of logical conjunctions.
| Input 1 | Input 2 | output |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
OR gate:
An OR gate is a digital logic gate that produces a ‘1’ output when at least one of its input signals is ‘1’, and a ‘0’ output when all of its input signals are ‘0’.
We need to take two or more inputs to an OR gate, and we get only one output of each preposition or value we specified in the truth table. The OR gate implements the Boolean function of logical disjunctions.
| Input 1 | Input 2 | output |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
NOT gate:
A NOT gate, also known as an inverter is a simple logic gate. This system takes one input and produces one output. The output of a NOT gate is the logical complement to its input, which means that if the input preposition or value is ‘0’ than the output preposition or value will be ‘1’.
NOT gate implements the Boolean function of logical negation.
| Input | output |
| T | F |
| F | T |
In simple words, we can say that NOT gate is a logic gate which can convert TRUE into FALSE and FALSE into TRUE, also ‘0’ into ‘1’ and ‘1’ into ‘0’, also YES into NO and NO into YES.
Examples:
Some examples of AND, OR, and NOT gate are as follows. By understanding of these examples you would be able to understand the concept of Boolean algebra.
Example 1:
Make a truth table of AND gate by using the Boolean expression.
Solution:
| A | B | A*B |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 0 |
In the above example of AND gate we used the Boolean expression as a preposition and you can clearly see that the result of AND logic gate in the form of Boolean expression. Let us describe the detail of above-mentioned example.
Step 1:
In this step, we took the preposition as a Boolean expression. And we used two inputs as a preposition which is ‘A’ and ‘B’.
Step 2:
In this step, the operation according to the given condition is applied to the given preposition.
Step 3:
In this step, we get the output of the given prepositions in the form of a result.
Example 2:
Make a truth table of OR gate by using the Boolean expression.
Solution:
| A | B | A+B |
| 1 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
In the previous example, we used a Boolean expression as the condition for the gate. The OR gate takes two inputs and produces a single output based on the logical disjunction of the two points.
The result of the OR gate is also represented as a Boolean expression, which indicate weather the output or result is ‘1’ or ‘0’. Let us describe the detail of this example to gain a better understanding of the functioning of OR gate.
Step 1:
In this step, we took the preposition as a Boolean expression. And we used two inputs as a preposition which is ‘A’ and ‘B’. But, here we applied the operation of an OR gate.
Step 2:
In this step, according to the given condition operation would be applied on a given preposition.
Step 3:
In this step, we got the result of given preposition in the form of output.
Example 3:
Make a truth table of NOT gate by using the Boolean expression.
Solution:
| A | A! |
| 1 | 0 |
| 0 | 1 |
To illustrate the functioning of a NOT gate, we previously utilized a Boolean expression as the gate’s input condition. This gate operates on one input signals, evaluating whether it is ‘1’ or ‘0’, and then generate a single output signal based on their logical negation.
The output signal of NOT gate is represented as a Boolean expression, which reflects its status as it is ‘1’ or ‘0’. Let us describe the detail of above-mentioned example to gain the better understanding of the function of NOT gate.
Step 1:
In this step, we only took one preposition as an input in the form of Boolean expression.
Step 2:
In this step, according to the given condition operation would be applied on a given preposition.
Step 3:
In this step, we got the result of given preposition in the form of output.
You can try a Boolean calculator by Calculators.tech to get avoid manual calculations.
Applications of Boolean algebra
Some applications of Boolean algebra are as follows:
- Digital electronics
- Computer programming
- Database system
- Search engines
- Home automation system
- Game design
Overall, Boolean algebra has numerous applications in various fields and plays a crucial role in the modern technology and innovation.
Conclusion:
In this article, we discussed the introduction, definition, types of Boolean algebra, their applications in daily life and also try to understand the concept of Boolean algebra through examples. After a complete go through of this article everyone would be able to understand the concept of logic gates.
Boolean algebra plays very important role in the current advancement of the modern technology and innovation. Also, it is using in different fields of science.