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Luhn algorithm. The Luhn algorithm or Luhn formula, also known as the " modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers. It is described in US patent 2950048A, granted on 23 August 1960. [1]
The algorithmic state machine (ASM) is a method for designing finite state machines (FSMs) originally developed by Thomas E. Osborne at the University of California, Berkeley (UCB) since 1960, [1] introduced to and implemented at Hewlett-Packard in 1968, formalized and expanded since 1967 and written about by Christopher R. Clare since 1970. [2 ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
State diagram In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S 1 (the first row) and receives an input of 1 (second column), the machine will stay in the state S 1 .
Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the ...
A classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q 0, F): [2] [3] Vertices Q: a finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them; Input symbols Σ: a finite collection of input symbols or designators
An electronic counter is a sequential logic circuit that has a clock input signal and a group of output signals that represent an integer "counts" value. Upon each qualified clock edge, the circuit will increment (or decrement, depending on circuit design) the counts. When the counts have reached the end of the counting sequence (maximum counts ...