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This is another post regarding the just basic overview of Digital electronics. The detailed part would have been too lengthy if I would have written here. Therefore, the left part will be available in my coming articles.
So let's visit the post and start learning....
BOOLEAN ALGEBRA:
Boolean algebra is mathematics of logic. It is one of the most basic tools which is used in the analysis and synthesis of logic circuit. In Boolean algebra, often the variables are represented by capital letters
such as A, B, C , X , Y , Z . The Boolean value of a variable is either logic 0 or logic 1. These, 0 and 1, are known as Boolean constants.
Logic Levels:
Boolean logic variable ‘0’ or ‘1’ is not used to represent actual numbers
but it is used to represent the state of voltage variable called logical level.
BASIC BOOLEAN OPERATIONS:
Boolean algebra uses only three basic operations, namely
- OR operation
- AND operation
- NOT operation
Boolean Addition (Logical OR):
The OR operation in Boolean algebra is similar to addition in ordinary
algebra i.e., OR means logical addition operation. The logical OR
operation on A and B is denoted by Y = A+B, where ‘+’ is the OR operator
The output Y corresponding to various combinations of inputs, A and B.
Boolean Multiplication (Logical AND):
The AND operation in Boolean algebra is similar to multiplication in
ordinary algebra i.e, AND performs logical multiplication operation.
Let A and B be two Boolean variables. Then, the logical AND
operation on A and B is denoted by
Y = A.B,
where (.) is the AND operator. The output Y corresponding to various
combinations of inputs, A and B.
Logical NOT:
NOT is the simplest of the three basic operations of Boolean algebra.
It is also known as inversion and complement. The NOT operation is
indicated by a bar ‘-’ over the variable. If A is a variable, then NOT
of A is expressed as A .
THEOREMS OF BOOLEAN ALGEBRA:
The theorems of Boolean algebra can be used to simplify many complex
Boolean expression and also to transform the given expression into a more useful and meaningful equivalent expression. These theorems are discussed as below.
Complementation Laws:
The term complement implies to invert, i.e. to change 1’s to 0’s and 0’s
to 1’s. The five laws of complementation are as follows:
- The complement of 0 is 1,
- The complement of 1 is 0,
- If A = 0, then A = 1
- If A = 1, then A = 0
- The double complementation does not change the function.
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For the first part till here only. I will be back with the next part soon.
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