
Boolean algebra is a system of logic dealing with variables that can have only two values:
True (represented by 1) and False (represented by 0). It provides a framework for reasoning and simplifying logical expressions, similar to how regular algebra works with numbers. Analysing digital gates and circuits is done with it. Performing a mathematical operation on binary numbers, or "0" and "1," makes sense. Basic operators in Boolean algebra include AND, OR, NOT, and so forth. The symbols "." for AND and "+" for OR denote operations. Variables that are represented by capital letters, such as "A," "B," and so forth, can be subjected to operations.
Properties of Boolean algebra –
Annulment law – a variable ANDed with 0 gives 0, while a variable ORed with 1 gives 1,
e.g.
A.0 = 0
A + 1 = 1
Identity law – in this law variable remains unchanged it is ORed with ‘0’ or ANDed with ‘1’,
e.g.
A.1 = A
A + 0 = A
Idempotent law – a variable remains unchanged when it is ORed or ANDed with itself,
e.g.
A + A = A
A.A = A
Complement law – in this Law, if a complement is added to a variable it gives one, if a variable is multiplied by its complement it results in ‘0
e.g.
A + A' = 1
A.A' = 0
Double negation law – a variable with two negations, its symbol gets cancelled out and the original variable is obtained,