Binary Logic
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Transcript of Binary Logic
Binary Logic
• Binary logic deals with variables that take on discrete values (e.g. 1, 0) and with operations that assume logical meaning (e.g. AND, OR and NOT)
George Boole
• An English Mathematician• An inventor of Boolean Logic• Boolean logic=Basis of computer logic• His work was re-discovered byClaude Shannon 70 years afterBoole’s death
Associative Law
• A+(B+C)=(A+B)+C• (A ∙ B) ∙ C=A ∙(B∙C)• Interpretation: we can group the
variables in AND or OR any way we want
• Example:– 1+(1+0)=(1+1)+0– (1∙ 0)0=1(1∙0)
Distributive Law
• X ∙(Y+Z)=X ∙ Y+X ∙ Z• (W+X)(Y+Z)=W ∙ Y+X ∙ Y+W ∙ Z+X
∙ Z• In Plain English: An expression can
be expanded by multiplying term by term just as in ordinary algebra
• Example:– 1 ∙(1+0)=1 ∙ 1+1 ∙ 0
Commutative Laws
• X+Y=Y+X• X ∙ Y=Y ∙ X• In Plain English: The order in which
we OR or AND two variables are not important
• Example– (1+0)=(1+0)
Duality
• If the dual of an algebraic expression is desired, we simply – Interchange OR and AND– Interchange 1 and 0
• Example– A+(B+C)=(A+B)+C– (A ∙ B) ∙ C=A ∙(B∙C)
Logic Gates• Logic gates are electronic circuits
that operate on one or more input signals to produce signals
NOT Operation
Not x is equal to x’
Interpretation:x’ is what x is not
x’ performs the complement operation