Talha's Physics Academy
Exclusive Logic Gates: XOR and XNOR Gates
Video Lecture: XOR and XNOR Gates
Watch the complete video lecture explaining the definitions, boolean expressions, and truth tables of XOR and XNOR gates:
6. XOR Gate (Exclusive-OR Gate)
“The logic gate which produces a high output only when high inputs are in odd number is known as Exclusive OR Gate (XOR Gate).”
Boolean Expressions
- Two Inputs: $X = A \oplus B = \bar{A}B + A\bar{B}$
- Three Inputs: $X = A \oplus B \oplus C$
- Four Inputs: $X = A \oplus B \oplus C \oplus D$
Fig: Logic symbols for XOR gates.
Truth Tables
i) Two Inputs
| Input | Output | |
|---|---|---|
| A | B | X |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
ii) Three Inputs
| Input | Output | ||
|---|---|---|---|
| A | B | C | X |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
iii) Four Inputs
| Input | Output | |||
|---|---|---|---|---|
| A | B | C | D | X |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 |
7. XNOR Gate (Exclusive-NOR Gate)
“The logic gate which produces a high output only when high inputs are in even number is known as Exclusive NOR Gate (XNOR Gate).”
Boolean Expressions
- Two Inputs: $X = \overline{A \oplus B} = AB + \bar{A}\bar{B}$
- Three Inputs: $X = \overline{A \oplus B \oplus C}$
- Four Inputs: $X = \overline{A \oplus B \oplus C \oplus D}$
Fig: Logic symbols for XNOR gates.
Truth Tables
i) Two Inputs
| Input | Output | |
|---|---|---|
| A | B | X |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
ii) Three Inputs
| Input | Output | ||
|---|---|---|---|
| A | B | C | X |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
iii) Four Inputs
| Input | Output | |||
|---|---|---|---|---|
| A | B | C | D | X |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
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