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In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function. The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions.
The size of a circuit is the number of gates it contains and its depth is the maximal length of a path from an input gate to the output gate. There are two major notions of circuit complexity. [1] The circuit-size complexity of a Boolean function is the minimal size of any circuit computing .
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits of polynomial size. Comparator circuits are sorting networks in which each comparator gate is directed, each wire is initialized with an input variable, its negation, or a constant, and one ...
In 1984 Furst, Saxe, and Sipser showed that calculating the parity of the input bits (unlike the aforementioned addition/subtraction problems above which had two inputs) cannot be decided by any AC 0 circuits, even with non-uniformity. [5] [1] It follows that AC 0 is not equal to NC 1, because a family of circuits in the latter class can ...
Comparators are closely related to operational amplifiers, but a comparator is designed to operate with positive feedback and with its output saturated at one power rail or the other. If necessary, an op-amp can be pressed into service as a poorly performing comparator, but its slew rate will be impaired.
In most cases a comparator is implemented using a dedicated comparator IC, but op-amps may be used as an alternative. Comparator diagrams and op-amp diagrams use the same symbols. A simple comparator circuit made using an op-amp without feedback simply heavily amplifies the voltage difference between Vin and VREF and outputs the result as Vout.
If the circuit C outputs A∧B for circuits A and B, join the branching programs that γ-compute A, δ-compute B, γ −1-compute A, and δ −1-compute B for a choice of 5-cycles γ and δ such that their commutator ε=γδγ −1 δ −1 is also a 5-cycle. (The existence of such elements was established in Lemma 2.)
LM393 differential comparator manufactured by National Semiconductor. The following is a list of LM-series integrated circuits.Many were among the first analog integrated circuits commercially produced since late 1965; [1] some were groundbreaking innovations [opinion].