binary logic
DESCRIPTION
Binary Logic. Section 1.9. 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). Home Alarm Logic. W1, W2, P and D are variables which can take on discrete values. - PowerPoint PPT PresentationTRANSCRIPT
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