Understanding Boolean Algebra

2 min readJul 29, 2024

Boolean Algebra is a fascinating form of algebra completely different from the one you use as part of Mathematics. Named after George Bool, who was the first person to describe this system and manipulate it easily, it is a system of mathematical logic, used to create logical expressions and statements, which can have 2 values.

The 2 Values Of Boolean Logic

Boolean statements can have two values, i.e. 0 and 1. Now, this can be represented in various ways, i.e., True, Yes or High (voltage) for 1 and False, No and Low (voltage) for 0.

What are Logical Statements?

In simple words, logical statements are statements that can be evaluated as either True or False. They can be sentences, or even expressions.
For example-

1. Delhi is located in India.
2. 2+8=19
3. What are you doing?

Here, the statements 1. and 2. can be answered using True/False. Hence, they are logical statements. However, 3. cannot be answered using only True/False. So, it is not a logical statement.

Logical statements are also called truth functions or boolean expressions.

Here are a few examples of the type of boolean expressions that you will commonly find-

A AND B
A OR B
NOT A

Truth Values

Truth values are basically, the values True and False, that are used to evaluate truth functions. Each truth function can take either of these two values (True and False).

The variables that can store these values are called logical variables or binary valued variables.

Truth tables-

Truth tables are another import component of Boolean Algebra that you should know. In simple words; A truth table is a table that represents all the possible values of the logical variables or expressions, along with all the possible results of the given combination of values.

Here’s an example of an expression along with its truth table-