XOR Gates#
Definition: XOR Gate
A XOR gate is a logic gate which computes the exclusive disjunction.
Notation
The following symbols are used for XOR gates:
Here is the truth table for this gate:
| \(A\) | \(B\) | \(\mathop{\operatorname{XOR}}(A, B)\) |
|---|---|---|
| \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) |
CMOS Implementation#
Implementing a XOR gate via CMOS is done using the following formula:
\[A \oplus B = \overline{(A+\overline{B})(\overline{A}+B)}\]
This formula is the negation of the function \((A+\overline{B})(\overline{A}+B)\). This means that we can follow the standard procedure for designing a CMOS which implements \((A+\overline{B})(\overline{A}+B)\), but we can omit the inverter at the end.
