ICTFundamental ConceptHSC আইসিটি অধ্যায় ৩ (সংখ্যা পদ্ধতি ও ডিজিটাল লজিক)

Boolean Algebra

Bengali: বুলিয়ান অ্যালজেবরা•Pronunciation: বুলিয়ান অ্যালজেবরা•Symbol: 0, 1 \text{ ও } \cdot, +, \overline{A}

Standard Definition:

The branch of mathematics in which the values of the variables are the truth values true (1) and false (0).

📐 Mathematical Equation, Units & Dimensions

Defining Mathematical Equation

\overline{A+B} = \overline{A} \cdot \overline{B}, \text{ } \overline{A \cdot B} = \overline{A} + \overline{B}

Standard SI Unit

Logical state (0 / 1)(যৌক্তিক মান (True/False))

Dimensional Analysis

[M^0 L^0 T^0]

CGS Unit

None

📖 Physical Concept & Comprehensive Explanation

Founded by George Boole, Boolean algebra governs all binary digital logic circuits. Its three primitive operators are AND, OR, and NOT. De Morgan's laws provide foundational tools for logic minimization.

🎯 High-Yield Revision Points

✓Operates exclusively on binary states: 0 and 1.
✓3 core logic operators: AND, OR, and NOT.
✓De Morgan's laws enable circuit minimization.

Use Online Solver for Boolean Algebra

Compute step-by-step solutions, verify formulas, and plot interactive diagrams on biggan.me.

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❓ Frequently Asked Exam Questions (FAQ)

Common questions in board and competitive entrance examinations

Q1: State De Morgan's two laws.

1st Law: ~(A + B) = ~A * ~B. 2nd Law: ~(A * B) = ~A + ~B.

Related STEM Terms

Logic Gateলজিক গেট • ICT

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Truth Tableসত্যক সারণি • ICT

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