Questions and Answers
What is the simplification rule?
A (A'B) = AB; A+(A'B) = A+B
What does the absorption rule state?
A (A+B) = A; A+(AB) = A
What is the distributive property in Boolean algebra?
A (B+C) = (AB)+(AC); A+(BC)= (A+B)(A+C)
What is DeMorgan's theorem?
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What does the union operation state?
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What is the null element?
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What is the complementary rule?
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What is the involution rule?
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What defines the idempotent law?
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What does the associative law state?
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What is the commutative law?
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What is the identity element for addition and multiplication?
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What signifies idempotency in Boolean algebra?
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What does NAND gate represent algebraically?
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What is a maxterm in Boolean algebra?
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What is a minterm?
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Study Notes
Boolean Algebra Theorems and Concepts
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Simplification:
- A (A'B) simplifies to AB.
- A + (A'B) simplifies to A + B.
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Absorption:
- A (A + B) reduces to A.
- A + (AB) simplifies to A.
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Distributive Law:
- A (B + C) equals (AB) + (AC).
- A + (BC) equals (A + B)(A + C).
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DeMorgan's Theorem:
- The expression A'B' transforms to A' + B' (AND to OR).
- The expression A' + B' transforms to A'B' (OR to AND).
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Union:
- A + 1 results in 1.
- A + 0 equals A.
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Null Law:
- A * 0 equals 0.
- A + 1 equals 1.
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Complementary Law:
- A * A' results in 0.
- A + A' equals 1.
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Involution Law:
- A'' simplifies back to A.
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Idempotent Law:
- A * A equals A.
- A + A equals A.
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Associative Law:
- A(BC) simplifies to ABC.
- A + (B + C) simplifies to A + B + C, demonstrating that grouping does not affect results.
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Commutative Law:
- AB equals BA.
- A + B equals B + A, showing order does not matter.
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Identity Law:
- A + 0 equals A.
- A * 1 equals A, indicating the identity elements for addition and multiplication.
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Inverse Law:
- Identifies that the inverse element produces the identity; 0 for OR and 1 for AND.
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Idempotency:
- Identical inputs in OR or AND gates yield the original value, indicating redundancy.
Logic Gates
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NAND Gate:
- The operation is represented by (A * B)'.
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OR Gate with Inverted Inputs:
- Expressed as A' + A'.
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AND Gate with Inverted Inputs:
- Written as A' * B'.
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NOR Gate:
- Represented by (A + B)'.
Canonical Forms
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Sum-of-Products (SOP):
- Consists solely of maxterms, representing a disjunction (OR) of minterms.
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Product-of-Sums (POS):
- Composed only of minterms, indicating a conjunction (AND) of maxterms.
Minterms and Maxterms
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Minterm:
- A Boolean expression that results in an output of 1 for a single cell in a Karnaugh map or truth table, outputs 0 elsewhere.
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Maxterm:
- A Boolean expression that results in an output of 0 for a single cell in a Karnaugh map or truth table, outputs 1 elsewhere.
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Description
Test your knowledge of Boolean Algebra with these flashcards highlighting key theorems and simplifications. Each card presents a fundamental concept such as simplification, absorption, and DeMorgan's laws. Perfect for students and professionals looking to strengthen their understanding of digital logic.
