When we talk about Algebra, our mind recalls the basic operation of +, -, / and x , as well as the ( ) and = operators. Variables and numbers "fly" over the "= " symbol during maths solving. These are basic algebra we learn in elementary school. However, there is another school of algebra that caters to a special application.
This special case of algebra is called Boolean Algebra.
What is so special about it?
It is a special because it invovles some concept that is unique, and is customised towards digital electronics engineering, meaning, it is of base 2.
Rules are aplenty in Boolean Algebra. In fact, it is a list quite similar to the normal Algebra with its Distributive and Associative Laws.
However, being base 2, users have to be aware that the answer to the maths operation is ON or OFF only, nothing in between.
To have a glimpse of what Boolean Algebra is about, below is some examples with explanations.
Boolean Algebra requires some inputs to get some outputs. Let call the inputs A and B, and the output as Y. (For a case example of 2 inuts and 1 output).
Case 1: A . A = A (not A2)
The reason for above is when a ligh bulb is On twice, it is still On. Note, outcome is either On or Off, nothing in between like double On.
Case 2: For an operation with A(A + B) = Y ==> A.A + AB = Y ==> A + AB = Y
If we factorised the above, we get A(1 + B) = Y.
But (1 + B) means the operation is always on, therefore (1 + B) = 1.
This leads us to the conclusion that A(A + B) = Y ===> A (1) = Y ==> A = Y
Did you feel the conceptual analysis of Boolean Algebra for the above examples?
If you are able to follow the reasonings, you will see that Boolean Algebra is really a special set of Algebra that caters to a special needs. From here, we can feel the power of learning maths.
Maths is so diversified, flexible, and borderless that with some twist to its basics, we can customise their usage to some special applications.
Isn't maths wonderful and powerful?
It amazes me for its great incredibility! Maths is GREAT!