Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity. Any single variable can have a 1 or a 0 value. The complement is the inverse of a variable and is indicated by a bar over var

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Examples in Boolean Expression Simplification:
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C + (BC)

Expression Rule(s) Used
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C + (BC) Original Expression
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C + (B + C) DeMorgan's Law
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(C + C) + B Commutative, Associative Laws
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1 + B Compliment Law

1 Identity Law

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(AB)(A + B)(B + B)

Expression Rule(s) Used
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(AB)(A + B)(B + B) Original Expression
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(AB)(A + B)(1) Compliment law, Identity law
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(A + B)(A + B) De Morgan's Law (AND with 1 was dropped because A*1=A)
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A A + A B + B A + B B Distributive Law
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A + A(B + B) + 0 Redundancy (on As), Identities
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A + A(1)
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A

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(A + C)(AD + AD) + AC + C

Expression Rule(s) Used
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(A + C)(AD + AD) + AC + C Original Expression
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(A + C)A(D + D) + AC + C Distributive.

(A + C)A + AC + C Compliment, Identity.

AA + AC + AC + C Distributive.

A + AC + C Redundancy

A + C + C Identity (A + AC = A + C)

A + C Redundancy


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(A)(A + B) + (B + A)(A + B)

Expression Rule(s) Used
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(A)(A + B) + (B + A)(A + B) Original Expression
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(A)A + (A)B + (B + A)A + (B + A)(B) Distributive
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(A)B + (B + A)A + (B + A)(B) AA = 0
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(A)B + BA + AA + B(B) + A(B) Redundancy and Identity
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