NIMCET Boolean Algebra Notes: Laws, Formulas, Logic Gates
Boolean algebra is an important topic in the Computer Awareness section of NIMCET. It deals with binary values (0 and 1), logical operations, Boolean expressions and truth tables. Understanding these concepts helps students solve logic-based questions accurately and improve their performance in the exam.
As part of the NIMCET syllabus, Boolean algebra covers logic gates such as AND, OR, NOT, NAND, NOR and XOR, along with Boolean laws and expression simplification. With regular practice, revision of key formulas and solving multiple-choice questions, students can strengthen their understanding and prepare effectively for this topic.
Basic Laws and Formulas for NIMCET Boolean Algebra
These NIMCET Boolean Algebra formulas help you cut long expressions into short ones. Most simplification questions use only the laws given in the table.
|
Law |
Rule |
|
Identity |
A + 0 = A and A · 1 = A |
|
Null |
A + 1 = 1 and A · 0 = 0 |
|
Idempotent |
A + A = A and A · A = A |
|
Complement |
A + A' = 1 and A · A' = 0 |
|
Double negation |
(A')' = A |
|
Commutative |
A + B = B + A and A · B = B · A |
|
Distributive |
A · (B + C) = A·B + A·C and A + B·C = (A + B)(A + C) |
|
Absorption |
A + A·B = A and A · (A + B) = A |
|
Useful result |
A + A'·B = A + B |
|
De Morgan's |
(A + B)' = A' · B' and (A · B)' = A' + B' |
De Morgan's laws are asked very often. A simple way to remember them: break the bar, and change the sign between the variables.
Logic Gates You Must Know for NIMCET
A logic gate takes one or more inputs (0 or 1) and gives one output. NIMCET logic gates are the base of most questions in this topic, so learn the rule of each gate by heart.
|
Gate |
Expression |
Rule |
|
AND |
A · B |
Output is 1 only when all inputs are 1 |
|
OR |
A + B |
Output is 1 when at least one input is 1 |
|
NOT |
A' |
Output is the opposite of the input |
|
NAND |
(A · B)' |
Output is the opposite of AND |
|
NOR |
(A + B)' |
Output is the opposite of OR |
|
XOR |
A ⊕ B |
Output is 1 when the two inputs are different |
The truth table below shows the output of each two-input gate for every input pair. Learn it once, and you can answer many questions in seconds.
|
A |
B |
AND |
OR |
NAND |
NOR |
XOR |
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
|
0 |
1 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
0 |
0 |
0 |
NAND and NOR are called universal gates. This means any other gate can be made using only NAND gates or only NOR gates. For example, if you join both inputs of a NAND gate together, it works as a NOT gate.
How to Simplify Boolean Expressions Step by Step
Simplifying means making an expression shorter without changing its meaning. Follow the same steps each time, and you will make fewer mistakes.
Take the expression AB + AB' + A'B.
-
Take A common from the first two terms: A(B + B') + A'B.
-
Use the complement law, B + B' = 1. The expression becomes A + A'B.
-
Use the useful result, A + A'B = A + B.
So the answer is A + B. If the question gives options, you can also test two or three input values to confirm your answer quickly.
NIMCET Boolean Algebra Notes PDF
NIMCET Boolean Algebra Notes PDF covers the basic laws, rules, Boolean expressions, and logic operations important for Computer Awareness preparation. Students can use these notes to revise key concepts, understand Boolean algebra identities, and practise questions for the NIMCET exam.
NIMCET Boolean Algebra Notes PDF -1
NIMCET Boolean Algebra Notes PDF -2
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NIMCET Boolean Algebra Notes PDF -3
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How to Prepare Boolean Algebra for NIMCET
A short and steady plan works better than long study hours. Boolean algebra can be finished in about a week if you give it a little time each day.
-
Make your own NIMCET Boolean Algebra notes with the gate table, truth table and laws on one or two sheets.
-
If you want a NIMCET Boolean Algebra PDF, pick one made for the 2026 syllabus and avoid old files. The NIMCET previous year question papers show how the topic has been asked in the exams before.
-
Learn the laws first, then solve 10 to 15 questions every day.
-
Write the truth table of each gate by hand until you do not need to look at it.
-
Revise the notes once every three days, and take a short timed test at the end of the week.
-
Do not skip other scoring areas such as number systems. Refer to the important NIMCET computer topics to plan your time well.
Since negative marking applies, attempt a question only when you are sure of the rule behind it.
Boolean algebra is one of the easiest topics in NIMCET once the gates, truth tables and laws are clear. Regular practice of simple questions is all it needs. If you want expert help with the full syllabus, live classes and test practice, PW's NIMCET online coaching can support your preparation.
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