Input Controls
Live Display
| A | B | Output (Y = (A ⊕ B)') |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Current Observation
Set inputs A and B using the toggle switches and observe how the EX-NOR gate processes the signals. Output becomes HIGH when both inputs are equal.
Signal Flow Observation
Toggle the switches to observe the signal flow animation through the wires. Output becomes HIGH (1) when both inputs are identical (both 0 or both 1).
Definition
An EX-NOR (Exclusive-NOR or XNOR) gate is a digital logic gate whose output is HIGH (1) only when all of its inputs are equal (either all LOW or all HIGH). If the inputs are different, the output is LOW (0).
Working Principle
The XNOR gate performs Exclusive-OR (XOR) logic followed by logical inversion (NOT). It operates as a digital equivalence detector or comparator.
- When both inputs A and B are equal (0,0 or 1,1) → internal XOR is 0 → inverted to HIGH (1).
- When inputs A and B are different (0,1 or 1,0) → internal XOR is 1 → inverted to LOW (0).
Equivalence & Coincidence Detection
Because the XNOR gate produces a HIGH output whenever its inputs match, it is widely referred to as a Coincidence Logic Gate or Digital Equality Comparator.
Truth Table Summary
The 2-input XNOR gate has 4 input combinations. Two combinations with matching inputs (A=0, B=0 and A=1, B=1) produce HIGH output (1), while combinations with unequal inputs produce LOW output (0).
Boolean Expression
Y = (A ⊕ B)' (also written as Y = A ⊙ B or Y = A'B' + AB)
Industrial Applications
- Digital Equality Comparator: The output becomes HIGH only when both inputs are identical. Used in microprocessors and digital circuits to compare binary data words.
- Parity Generators and Checkers: Used in data transmission and error detection circuits (e.g. RAM, bus systems) to maintain even parity.
- Phase Detectors: Employed in Phase-Locked Loops (PLL) to detect frequency and phase alignment between reference and feedback clock signals.
- Cryptographic & Authentication Circuits: Performs bitwise comparison and hash key verification in secure digital systems.
- ALU Magnitude Comparison: Serves as the core bit-level equality detector in Arithmetic Logic Units (ALUs).
Boolean Expression
Y = (A ⊕ B)'
The apostrophe (') represents the inversion of the Exclusive-OR (⊕) operation. It can also be expressed with the equivalence symbol: Y = A ⊙ B.
Canonical SOP & POS Forms
In Sum of Products (SOP) form:
Y = A'B' + AB
In Product of Sums (POS) form:
Y = (A + B')(A' + B)
Boolean Properties of XNOR
- Self-Equivalence: A ⊙ A = 1
- Inversion Relation: A ⊙ A' = 0
- Identity Element: A ⊙ 1 = A
- Inverter (via 0): A ⊙ 0 = A'
- Commutative Law: A ⊙ B = B ⊙ A
- Complement of XOR: (A ⊕ B)' = A ⊙ B
Current Calculation
A = 0, B = 0 → Y = (0 ⊕ 0)' = 1
Digital Equality Comparator
The output becomes HIGH only when both inputs are identical.
This XNOR gate logic verifies binary data equality. When Input Bit A equals Input Bit B (both 0 or both 1), the comparator outputs HIGH (1) indicating a MATCH.