Logic Gates

Basic Gates: NOT, AND & OR

Universal Gates: NAND & NOR

Arithmetic Gates: X-OR & X-NOR

NOT Gate

symbol, equation, and truth table.

AND Gate

If any of the input is low then the output is low.

Output is high (1) only when all the inputs are high, otherwise low (0)

Symbol

\(Equation : Y=a.b\)

Truth table

Associative Law : \(A.(B.C)=(A.B).C\)

Commutative Law : \(A.B=B.A\)

OR Gate

Output is high when any one or all inputs are low.

Output is low if all the input is low, otherwise output is high.

Symbol

\(Equation : Y=a+b\)

Truth table

Associative Law : \(A+(B+C)=(A+B)+C\)
Commutative Law : \(A+B=B+A\)

NAND Gate

\(Equation : Y=\overline{(a.b)}\)

NOR Gate

\(Equation : Y=\overline{(a+b)}\)

Exclusive OR Gate (EX-OR/XOR)

Odd 1’s detector. This Means Output = 1, if the number of 1 at the input is odd.

\(\oplus\)

\(Equation : Y=a\overline{b}+\overline{a}b\)

\(\begin{aligned}Equation : Y&=a\oplus b \\ &=a\overline{b}+\overline{a}b \end{aligned}\)

Exclusive NOR Gate

\(\begin{aligned}Equation : Y&=a\odot b \\ &=ab+\overline{ab}\end{aligned}\)

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