equivalence gate
a logic gate performing a Boolean logic equivalence operation; an XNOR gate.
equivalence gate: XNOR logic that outputs true when inputs match
An equivalence gate is a digital logic circuit that compares two binary inputs and produces a single output. The output is high (1) when both inputs are identical, and low (0) when they differ. This makes it the logical inverse of an XOR gate, which is why it is also called XNOR, or exclusive NOR.
The truth table for a two-input equivalence gate shows the pattern clearly: inputs 0,0 yield output 1; inputs 0,1 yield 0; inputs 1,0 yield 0; inputs 1,1 yield output 1. In Boolean algebra, the equivalence function is written as A XNOR B or sometimes A ≡ B. Multi-input versions exist: a three-input equivalence gate outputs 1 only when an even number of its inputs are high, including zero.
Implementation and variants
Equivalence gates are built from basic logic primitives: typically two NOT gates, two AND gates, and one OR gate. In integrated circuits, XNOR gates are implemented directly at the transistor level, commonly using CMOS technology where they require fewer gates than constructing them from discrete XOR and NOT functions. Standard logic families like 74LS, 74HC, and 74AC include dedicated XNOR chips with two, three, or four independent gates per package.
The equivalence gate is essential in digital systems that need to detect agreement or parity. Comparators use equivalence gates to check if corresponding bits in two numbers or data words are the same. Error detection circuits employ arrays of equivalence gates to verify that transmitted data matches received data. Parity checkers and some CRC implementations rely on XNOR logic to identify transmission errors.
In field-programmable gate arrays (FPGAs) and programmable logic controllers (PLCs), equivalence gates are realized through lookup tables or configured from simpler gates. Propagation delay through an equivalence gate is typically 5 to 10 nanoseconds in modern CMOS processes, making it suitable for high-speed signal processing and real-time control. The term equivalence reflects the Boolean property it implements: the output is true when the logical equivalence of the two inputs holds.