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theory, an integer circuit is a circuit model of computation in which inputs to the circuit are sets of integers and each gate of the circuit computes either
Integer_circuit
Model of computation
Boolean circuit are Boolean values, and the circuit includes conjunction, disjunction, and negation gates. The values in an integer circuit are sets
Circuit_(computer_science)
Topics referred to by the same term
Boolean circuit, a mathematical model for digital logic circuits Integer circuit, a mathematical object of computational complexity Circuit complexity
Circuit
checking Type inhabitation problem for simply typed lambda calculus Integer circuit evaluation Word problem for linear bounded automata Word problem for
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Combinational digital circuit
logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point
Arithmetic_logic_unit
Quantum algorithm for integer factorization
factor integers in polynomial time. However, Shor's algorithm shows that factoring integers can be done with a polynomial complexity circuit on an ideal
Shor's_algorithm
Electronic circuit
sine wave is applied to a nonlinear circuit, the resulting distortion creates harmonics; frequency components at integer multiples nf of the fundamental frequency
Frequency_multiplier
Binary representation for signed numbers
most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. As with the
Two's_complement
Combinational logic circuit
input states to a specific combination of output states. In addition to integer data inputs, some decoders also have one or more "enable" inputs. When
Binary_decoder
Circuit
{\displaystyle f_{out}={\frac {f_{in}}{N}}} where N {\displaystyle N} is an integer. Phase-locked loop frequency synthesizers make use of frequency dividers
Frequency_divider
Central computer component that executes instructions
introduction. The arithmetic logic unit (ALU) is a digital circuit within the processor that performs integer arithmetic and bitwise logic operations. The inputs
Central_processing_unit
Use of functions that call themselves
recursion. An example is computing the factorial of an integer n, which is the product of all integers from 0 to n. For this problem, the definition 0! =
Recursion_(computer_science)
When a system's behavior depends on timing of uncontrollable events
software design. Assume that two threads each increment the value of a global integer variable by 1. Ideally, the following sequence of operations would take
Race_condition
Model of computational complexity
that the monotone NC hierarchy is infinite. The integer division problem lies in uniform TC0. Circuit lower bounds are generally difficult. Known results
Circuit_complexity
Counting circuit component
prescaler is an electronic counting circuit used to reduce a high frequency electrical signal to a lower frequency by integer division. The prescaler takes
Prescaler
Sinusoidal wave whose frequency is an integer multiple
voltage or current waveform is a sinusoidal wave whose frequency is an integer multiple of the fundamental frequency. Harmonic frequencies are produced
Harmonics_(electrical_power)
First model in the Apple II computer series
encoding of numbers in 16-bit integer format. Since it only supported integers between -32768 and +32767 (signed 16-bit integer), it was less suitable to
Apple_II_(original)
Programming language construct
order and optionally short-circuited In lua and OCaml, bitwise operators &, | (OCaml land, lor) are restricted to integers and cannot be used with Booleans
Short-circuit_evaluation
Measure of complexity of a Boolean circuit
problems weighted by a positive integer parameter k {\displaystyle k} solvable by circuits of weft bounded by a positive integer w {\displaystyle w} and arbitrary
Weft_(circuit)
Complexity class used in circuit complexity
default consider Boolean circuits with a polynomial number of AND, OR, NOT, and threshold gates, with polynomial bound on integer weights and thresholds
TC0
Complexity class
multi-collisions. For an integer t ≥ 2 {\displaystyle t\geq 2} , the problem t {\displaystyle t} -PIGEON asks, given a Boolean circuit representing a map from
PPP_(complexity)
64-bit RISC instruction set architecture
required to address 32 unique locations, the 32 integer registers. The integer literal format is used by integer instructions which use a literal as one of
DEC_Alpha
Vector representing lattice distortion due to dislocations in a crystal
this perfect crystal structure, a rectangle whose lengths and widths are integer multiples of a (the unit cell edge length) is drawn encompassing the site
Burgers_vector
Accomplishments in factoring large integers
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography
Integer_factorization_records
Mathematical problem
other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle
Squaring_the_square
Unsolved problem in computer science
input S IF the program outputs a list of distinct integers AND the integers are all in S AND the integers sum to 0 THEN OUTPUT "yes" and HALT This is a polynomial-time
P_versus_NP_problem
Topics referred to by the same term
former English shipbuilder Short circuit, an accidental connection between two nodes of an electrical circuit Short integer, a computer datatype Short film
Short
Computer architecture bit width
In computer architecture, 128-bit integers, memory addresses, or other data units are those that are 128 bits (16 octets) wide. Also, 128-bit central processing
128-bit_computing
Models replicating electronic behavior
Electronic circuit simulation uses mathematical models to replicate the behavior of an actual electronic device or circuit. Simulation software allows
Electronic_circuit_simulation
Programming language
Printing(output); var i : integer; procedure PrintAnInteger(j : integer); begin ... end; function triple(x: integer): integer; begin triple := x * 3 end;
Pascal_(programming_language)
Algorithm to multiply two numbers
this result is still not verified by the specialists of the subject. Integer multiplication algorithms can also be used to multiply polynomials by means
Multiplication_algorithm
Natural number
1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Kreweras, Germain (1978), "Complexité et circuits eulériens dans les sommes tensorielles
209_(number)
Encoding of negative numbers in binary number systems
criterion by which any of the representations is universally superior. For integers, the representation used in most current computing devices is two's complement
Signed_number_representations
Concept in quantum mathematics
lattice integer which connects a pair of qubits, and τ {\displaystyle \tau } is the time step. Figure 1, shows a time-space diagram of a quantum circuit which
Quantum_random_circuits
Short electrical transmission line
at one end only. The free end of the stub is either left open-circuit, or short-circuited (as is always the case for waveguides). Neglecting transmission
Stub_(electronics)
of 7400-series digital logic integrated circuits. In the mid-1960s, the original 7400-series integrated circuits were introduced by Texas Instruments with
List of 7400-series integrated circuits
List_of_7400-series_integrated_circuits
Type of positive integer
theory, a positive integer k is said to be an Erdős–Woods number if it has the following property: there exists a positive integer a such that in the
Erdős–Woods_number
Electronic circuit used to multiply binary numbers
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic
Binary_multiplier
Inherent difficulty of computational problems
or no. Notable examples include the traveling salesman problem and the integer factorization problem. It is tempting to think that the notion of function
Computational complexity theory
Computational_complexity_theory
Set of computational problems stated by Richard Karp (1973)
for formulas in conjunctive normal form (often referred to as SAT) 0–1 integer programming (A variation in which only the restrictions must be satisfied
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Multiplayer VR game (2016–2026)
form of integer input in order to keep track of players.[citation needed] In 2021, Rec Room introduced a more feature-rich version of the circuit system
Rec_Room_(video_game)
General-purpose programming language
integers and floats); e.g., "spam" + "eggs" returns "spameggs". If strings contain numbers, they are concatenated as strings rather than as integers,
Python_(programming_language)
Load measure in telecommunications
(which can be a non-integer such as 43.5) followed by "erlangs" represents the average number of concurrent calls carried by the circuits (or other service-providing
Erlang_(unit)
Arithmetical operation
generalizations of this basic definition define the multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers
Multiplication
Set of quantum operations
Encyclopedia of Integer Sequences. OEIS Foundation. Aaronson, Scott; Gottesman, Daniel (2004). "Improved simulation of stabilizer circuits". Physical Review
Clifford_group
Electronic circuit simulator software
CircuitLogix is a software electronic circuit simulator which uses PSpice to simulate thousands of electronic devices, models, and circuits. CircuitLogix
CircuitLogix
Electronic control system
recovery from a noisy communication channel. Since 1969, a single integrated circuit can provide a complete PLL building block, and nowadays has output frequencies
Phase-locked_loop
Complexity class of bounded-depth circuits
integers under the usual binary or base-10 representations of integers). Since it is a circuit class, like P/poly, AC0 also contains every unary language
AC0
Computer architecture bit width
In computer architecture, 8-bit integers or other data units are those that are eight bits wide (one octet). Also, 8-bit central processing unit (CPU)
8-bit_computing
Superconducting qubit architecture
It is a flux-like qubit, meaning that its energy levels correspond to integer numbers of magnetic flux/phase states. This architecture has long coherence
Fluxonium
Exponentation in modular arithmetic
is the remainder c when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c
Modular_exponentiation
Unproven computational hardness assumption
where n is the number of variables in the given k-SAT instance. For each integer k≥3, define sk to be the smallest number such that k-SAT can be solved
Exponential_time_hypothesis
Topics referred to by the same term
device that generates a signal at an integer multiple of its input frequency Voltage multiplier, an electrical circuit that converts AC electrical power
Multiplier
Frequencies used by electrical components
1,000,000), assuming a clock pre-divider of 16 is resolved to an exact integer baud rate. Though some UART variations have fractional dividers, those
Crystal oscillator frequencies
Crystal_oscillator_frequencies
Communication protocol property
a circuit switched connection, or a packet-mode virtual circuit connection. In the latter case, it may use either a transport layer virtual circuit protocol
Connection-oriented communication
Connection-oriented_communication
Branch of computational complexity theory
follows: There exists constant integers w,d, such that every instance (x,k) is transformed in fpt-time to a Boolean circuit that has weft at most w, and
Parameterized_complexity
Hardware acceleration unit for artificial intelligence tasks
capability. As of 2024[update], a widely used datacenter-grade AI integrated circuit chip, the Nvidia H100 GPU, contains tens of billions of metal–oxide–semiconductor
Neural_processing_unit
Physical characteristic of oscillating systems
2,3,\dots } where v {\displaystyle v} is the speed of the wave and the integer n {\displaystyle n} denotes different modes or harmonics. The standing
Resonance
Digital circuit that produces sums from inputs
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used in the arithmetic
Adder_(electronics)
Problem a computer might be able to solve
a positive integer n, find a nontrivial prime factor of n." is a computational problem that has a solution, as there are many known integer factorization
Computational_problem
Topics referred to by the same term
Primary ideals, concept in commutative algebra Primary number, positive integer power of a prime number Primary elections or primaries, elections held
Primary
Branch of elementary mathematics
Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers
Arithmetic
Digital circuit optimisation
circuit. Let d ( v ) {\displaystyle d(v)} be the propagation delay through vertex v {\displaystyle v} . The goal in retiming is to compute an integer
Retiming
Electronic circuit data format
capacitor. A capacitor lumped to ground has three fields: an identifying integer, a node name, and the capacitance value of this node. 1 regcontrol_top/GRC/U9743:E
Standard Parasitic Exchange Format
Standard_Parasitic_Exchange_Format
Programming language evaluation rules
none integer :: a = 1 integer :: b = 2 call Swap(a, b) print *, a, b ! 2 1 contains subroutine Swap(a, b) integer, intent(inout) :: a, b integer :: temp
Evaluation_strategy
Complex number representing a particular sine wave
can be used to (simultaneously) derive the transient response of an RLC circuit. However, the Laplace transform is mathematically more difficult to apply
Phasor
Condition determining when a linear electronic circuit will oscillate
criterion is a mathematical condition to determine when a linear electronic circuit will oscillate. It was put forth in 1921 by German physicist Heinrich Barkhausen
Barkhausen stability criterion
Barkhausen_stability_criterion
High-area shapes can shift to hold many grid points
to include at least ⌈ A ⌉ {\displaystyle \lceil A\rceil } points of the integer lattice. Equivalently, every bounded set of area A {\displaystyle A} contains
Blichfeldt's_theorem
Notation for expressing numbers
Ideally, a numeral system will: Represent a useful set of numbers (e.g. all integers, or rational numbers) Give every number represented a unique representation
Numeral_system
Trail in which only the first and last vertices are equal
simple circuit is a circuit in which v1,...,vn are distinct. n is called the length of the circuit resp. length of the cycle. A directed circuit is a non-empty
Cycle_(graph_theory)
Electronic oscillator circuit
at approximately odd integer multiples of the fundamental frequency. These are termed "overtone modes", and oscillator circuits can be designed to excite
Crystal_oscillator
Instructions a computer can execute
arithmetic logic unit (ALU). The ALU has circuits to perform elementary operations to add, shift, and compare integers. By combining and looping the elementary
Computer_program
Widely used standard for video compression
"Efficient prediction algorithm of integer DCT coefficients for H.264/AVC optimization". IEEE Transactions on Circuits and Systems for Video Technology
Advanced_Video_Coding
Form of encryption that allows computation on ciphertexts
were initially used to compute Boolean circuits over encrypted bits, but have been extended to support integer arithmetics and univariate function evaluation
Homomorphic_encryption
Equation of the form 1/a + 1/b = 1/c
the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c: 1 a + 1 b = 1 c . {\displaystyle {\frac
Optic_equation
Hardware description language
digital circuits, with the highest level of abstraction being at the register-transfer level. It is also used in the verification of analog circuits and mixed-signal
Verilog
Numbers obtained by adding the two previous ones
Fibonacci numbers Fn are: The Fibonacci sequence can be extended to negative integer indices by following the same recurrence relation in the negative direction
Fibonacci_sequence
Varying physical quantity that conveys information
a discrete-time (DT) signal is the set of integers (or other subsets of real numbers). What these integers represent depends on the nature of the signal;
Signal
House in United Kingdom, United Kingdom
available in every room, WebTV, and a closed-circuit television (CCTV) system. Furthermore, the INTEGER Millennium House included numerous innovative
INTEGER_Millennium_House
Electric current that periodically reverses direction
voltage. The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction
Alternating_current
Hypothesis in computational complexity theory
composite integer n {\displaystyle n} , and in particular one which is the product of two large primes n = p ⋅ q {\displaystyle n=p\cdot q} , the integer factorization
Computational hardness assumption
Computational_hardness_assumption
Study of mathematical algorithms for optimization problems
variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with
Mathematical_optimization
Programmable machine that processes data
cosine, etc., and square roots. Some can operate only on whole numbers (integers) while others use floating point to represent real numbers, albeit with
Computer
Mathematical problem
stated: Given positive integers a1,a2,…,ansuch that gcd(a1,a2,…,an)=1, find the largest integer that cannot be expressed as an integer conical combination
Coin_problem
Maximal independent set of the matroid
the independent sets are all sets with cardinality at most k (for some integer k), the bases are all sets with cardinality exactly k. In a partition matroid
Basis_of_a_matroid
Arithmetic operation
realization of full adder circuits, which in turn may be combined into more complex logical operations. In modern digital computers, integer addition is typically
Addition
Computer architecture bit width
In computer architecture, 256-bit integers, memory addresses, or other data units are those that are 256 bits (32 octets) wide. Also, 256-bit central processing
256-bit_computing
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Number expressed in the base-2 numeral system
representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with
Binary_number
Central processing unit by Sony Computer Entertainment and Toshiba
(Multimedia Extensions) was implemented by grouping the two 64-bit integer ALUs. Both the integer and floating-point pipelines are six stages long. To feed the
Emotion_Engine
Circuit simulation software
LTspice is a SPICE-based analog electronic circuit simulator computer software, produced by semiconductor manufacturer Analog Devices (originally by Linear
LTspice
Type of machine learning model
then integer indices are arbitrarily but uniquely assigned to each vocabulary entry, and finally, an embedding is associated with the integer index.
Large_language_model
Computational benchmark
Shor formulated Shor's algorithm, streamlining a method for factoring integers in polynomial time. In 1995, Christopher Monroe and David Wineland published
Quantum_supremacy
Fewest graph edges whose removal breaks all cycles
In graph theory, a branch of mathematics, the cyclomatic number, circuit rank, cycle rank, corank or nullity of an undirected graph is the minimum number
Cyclomatic_number
Functional square root of an exponential
exponential or logarithmic function iterated an integer number of times, rather than the half-integer that would be required for a half-exponential function
Half-exponential_function
Representation of a signal as a rectangular wave with varying duty cycle
sawtooth. The analog comparator of the intersecting method becomes a simple integer comparison between the current counter value and the digital (possibly
Pulse-width_modulation
Computational method
factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain
Factorization_of_polynomials
ordinary differential equations. Hadamard conjecture: for every positive integer k {\displaystyle k} , a Hadamard matrix of order 4 k {\displaystyle 4k}
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Concept in theoretical computer science
machine has n "operational" states plus a Halt state, where n is a positive integer, and one of the n states is distinguished as the starting state. (Typically
Busy_beaver
Topics referred to by the same term
cycle length of the ring's addition operation Characteristic (logarithm), integer part of a common logarithm Characteristic function, usually the indicator
Characteristic
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INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
INTEGER CIRCUIT
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