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The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the Exclusive OR gate. [1] It is equivalent to the logical connective ( ↔ {\displaystyle \leftrightarrow } ) from mathematical logic , also known as the material biconditional.
A standard LFSR has a single XOR or XNOR gate, where the input of the gate is connected to several "taps" and the output is connected to the input of the first flip-flop. A MISR has the same structure, but the input to every flip-flop is fed through an XOR/XNOR gate. For example, a 4-bit MISR has a 4-bit parallel output and a 4-bit parallel input.
Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments have the same truth value, and False if they are different.
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
An XNOR gate is a basic comparator, because its output is "1" only if its two input bits are equal. The analog equivalent of digital comparator is the voltage comparator . Many microcontrollers have analog comparators on some of their inputs that can be read or trigger an interrupt .
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
The XOR operation preserves randomness, meaning that a random bit XORed with a non-random bit will result in a random bit. Multiple sources of potentially random data can be combined using XOR, and the unpredictability of the output is guaranteed to be at least as good as the best individual source.
The gate is called XNOR because it is a NOR gate with an added twist. With NOR, if either or both inputs is 1, the output is 0. With XNOR, the "exclusive" condition is added to that, so that with XNOR, the output is 0 only if exactly one input is 1. With XNOR, the "both inputs 1" condition is excluded from producing the active output, namely 0.