Questions and Answers
Annulment Law - A term AND'ed with a '0' equals ___ or OR'ed with a '1' will equal ___.
0, 1
Identity Law - A term OR'ed with a '0' or AND'ed with a '1' will always equal that term. A + 0 = ___, A.1 = ___
A, A
Idempotent Law - An input that is AND'ed or OR'ed with itself is equal to that input. A + A = ___, A.A = ___
A, A
Complement Law - A term AND'ed with its complement equals '0' and a term OR'ed with its complement equals '1'. A.A' = ___, A + A' = ___
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Commutative Law - The order of application of two separate terms is not important. A + B = ___, A.B = ___
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What are the two 'de Morgan's' rules?
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What are Boolean Postulates?
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Distributive Law - This law permits the multiplying or factoring out of an expression. A(B + C) = ___, A + (B.C) = ___
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Absorptive Law - This law enables a reduction in a complicated expression to a simpler one by absorbing like terms. A + (A.B) = ___, A(A + B) = ___
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Associative Law - This law allows the removal of brackets from an expression and regrouping of the variables. A + (B + C) = ___, A(B.C) = ___
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What are Boolean Algebra Functions?
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Using the above laws, simplify the following expression: (A + B)(A + C)
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Study Notes
Annulment Law
- A term AND'ed with "0" results in 0: ( A \cdot 0 = 0 )
- A term OR'ed with "1" results in 1: ( A + 1 = 1 )
Identity Law
- A variable OR'ed with "0" equals the variable: ( A + 0 = A )
- A variable AND'ed with "1" equals the variable: ( A \cdot 1 = A )
Idempotent Law
- A variable OR'ed with itself equals the variable: ( A + A = A )
- A variable AND'ed with itself equals the variable: ( A \cdot A = A )
Complement Law
- A term AND'ed with its complement equals 0: ( A \cdot A' = 0 )
- A term OR'ed with its complement equals 1: ( A + A' = 1 )
Commutative Law
- The order of AND operation does not affect the result: ( A \cdot B = B \cdot A )
- The order of OR operation does not affect the result: ( A + B = B + A )
de Morgan's Theorem
- Two terms NOR'ed is equivalent to the inverted terms AND'ed: ( (A + B)' = A' \cdot B' )
- Two terms NAND'ed is equivalent to the inverted terms OR'ed: ( (A \cdot B)' = A' + B' )
Boolean Postulates
- ( 0 \cdot 0 = 0 )
- ( 1 \cdot 1 = 1 )
- ( 1 \cdot 0 = 0 )
- ( 0 + 0 = 0 )
- ( 1 + 1 = 1 )
- ( 1 + 0 = 1 )
Distributive Law
- OR Distributive Law: ( A(B + C) = A \cdot B + A \cdot C )
- AND Distributive Law: ( A + (B \cdot C) = (A + B)(A + C) )
Absorptive Law
- OR Absorption Law: ( A + (A \cdot B) = A )
- AND Absorption Law: ( A(A + B) = A )
Associative Law
- OR Associative Law: ( A + (B + C) = (A + B) + C = A + B + C )
- AND Associative Law: ( A(B \cdot C) = (A \cdot B)C = A \cdot B \cdot C )
Boolean Algebra Functions
- AND, OR, and NOT gates represent 16 possible Boolean functions.
Laws of Boolean Algebra Application
- Example of simplifying expressions by applying the above laws: ( (A + B)(A + C) ).
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Description
Test your knowledge on the laws of Boolean algebra with this quiz. Explore key concepts like the Annulment and Identity laws, and understand their definitions and applications. Perfect for students studying digital systems and related courses.
