Kodeclik Blog
The Absorption Law of Boolean Algebra
The Absorption Law is actually two laws that enable you to simplify boolean logic expressions.
First Absorption Law
When A is combined with the AND of A and B using OR operation, it simplifies to just A.
Second Absorption Law
When A is combined with the OR of A and B using AND operation, it simplifies to just A.
Why do these laws work? The law gets its name because one term effectively "absorbs" the other in the expression.
Let us take the first absorption law. Note that the main operation is an OR. So when A is true, the additional term becomes irrelevant to the final result which will be true. When A is false, both parts of the term will be false, so the overall result will be false. In both cases, the final result is the same as A!
Let us take the second absorption law now. When A is true, the first term in the AND (which is A) is true. The second term is also true (because it is an OR and one of its terms is A). Thus the overall result is true! When A is false, you can immediately see that the overall result will be false because a false AND anything is going to be false. So once again, the final result is the same as the truth value of A!
In both cases, the underlying theme is that one condition (here, A) is strong enough on its own to determine the outcome, making additional conditions (like B) unnecessary.
Verifying First Absorption Law using Truth Tables
You can also verify the first absorption law by exhaustively trying all 2x2=4 combinations. See below:
Verifying Second Absorption Law using Truth Tables
Again, here is a truth table to verify the second absorption law:
Summary
The Absorption Law is not just a cool trick—it’s super useful in real life, especially in things like designing circuits and writing code. By using this law, we can make complicated expressions much simpler, which saves time and resources. For example, when engineers create electronic devices like calculators or computers, they use this law to design circuits with fewer parts. Fewer parts mean the device is smaller, faster, and uses less power.
This law also helps in computer programming. When writing code with a lot of "if" statements, using the Absorption Law can make the code cleaner and easier to understand. It can also make programs run faster because the computer has to check fewer conditions. So, whether you’re solving a logic puzzle, programming a robot, or just trying to figure out how things work, the Absorption Law is a handy tool that makes life simpler!
