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Questions and Answers
Annulment Law - A term AND'ed with a '0' equals ___ or OR'ed with a '1' will equal ___.
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 = ___
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 = ___
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' = ___
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' = ___
Commutative Law - The order of application of two separate terms is not important. A + B = ___, A.B = ___
Commutative Law - The order of application of two separate terms is not important. A + B = ___, A.B = ___
What are the two 'de Morgan's' rules?
What are the two 'de Morgan's' rules?
What are Boolean Postulates?
What are Boolean Postulates?
Distributive Law - This law permits the multiplying or factoring out of an expression. A(B + C) = ___, A + (B.C) = ___
Distributive Law - This law permits the multiplying or factoring out of an expression. A(B + C) = ___, A + (B.C) = ___
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) = ___
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) = ___
Associative Law - This law allows the removal of brackets from an expression and regrouping of the variables. A + (B + C) = ___, A(B.C) = ___
Associative Law - This law allows the removal of brackets from an expression and regrouping of the variables. A + (B + C) = ___, A(B.C) = ___
What are Boolean Algebra Functions?
What are Boolean Algebra Functions?
Using the above laws, simplify the following expression: (A + B)(A + C)
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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