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