|
Toffoli Gate
In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli in 1980 is a CNOT gate with two control bits and one target bit. That is, the target bit (third bit) will be inverted if the first and second bits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. There is also a quantum-computing version where the bits are replaced by qubits. Description The truth table and permutation matrix are as follows (the permutation can be written (7,8) in cycle notation): Background An input-consuming logic gate ''L'' is reversible if it meets the following conditions: (1) ''L''(''x'') = ''y'' is a gate where for any output ''y'', there is a unique input ''x''; (2) The gate ''L'' is reversible if there is a gate ''L''´(''y'') = ''x'' which maps ''y'' to ''x'', for all ''y''. An example of a reversible logic gate is a NOT ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Circuits
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more Binary number, binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see ideal and real op-amps for comparison). The primary way of building logic gates uses diodes or transistors acting as electronic switches. Today, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). ''From Integrated circuit'' They can also be constructed using vacuum tubes, electromagnetic relays with relay logic, fluidic logic, pneumatics#Pneumatic logic, pneumatic logic, optics, molecular logic gate, molecules, acoustics, or even Analytical Engine, mechanical or thermal elements. Logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the constr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fredkin Gate
The Fredkin gate (also controlled-SWAP gate and conservative logic gate) is a computational circuit suitable for reversible computing, invented by Edward Fredkin. It is ''universal'', which means that any logical or arithmetic operation can be constructed entirely of Fredkin gates. The Fredkin gate is a circuit or device with three inputs and three outputs that transmits the first bit unchanged and swaps the last two bits if, and only if, the first bit is 1. Background The Fredkin gate, conceptualized by Edward Fredkin and Tommaso Toffoli at the MIT Laboratory for Computer Science, was a pivotal advancement in the field of reversible computing and conservative logic. Developed within the framework of conservative logic, the gate is designed to align computing processes with fundamental physical principles such as the reversibility of dynamical laws and the conservation of energy. The technical rationale behind the Fredkin gate is rooted in addressing the inefficiencies of tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a vectorial or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulo Operation
In computing and mathematics, the modulo operation returns the remainder or signed remainder of a Division (mathematics), division, after one number is divided by another, the latter being called the ''modular arithmetic, modulus'' of the operation. Given two positive numbers and , modulo (often abbreviated as ) is the remainder of the Euclidean division of by , where is the Division (mathematics), dividend and is the divisor. For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with and both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of is 0 to . mod 1 is always 0. When exactly one of or is negative, the basic definition breaks down, and programming languages differ in how these valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Van Leeuwen
Jan van Leeuwen (born 17 December 1946 in Waddinxveen) is a Dutch computer scientist and emeritus professor of computer science at the Department of Information and Computing Sciences at Utrecht University.Curriculum vitae , retrieved 2011-03-27. Education and career Van Leeuwen completed his undergraduate studies in mathematics at in 1967 and received a PhD in mathematics in 1972 from the same institution under the supervision of Dirk van Dalen.. After postdoctoral studies at the |
Functional Completeness
In Mathematical logic, logic, a functionally complete set of logical connectives or Boolean function, Boolean operators is one that can be used to express all possible truth tables by combining members of the Set (mathematics), set into a Boolean expression.. ("Complete set of logical connectives").. ("[F]unctional completeness of [a] set of logical operators"). A well-known complete set of connectives is . Each of the singleton (mathematics), singleton sets and is functionally complete. However, the set is incomplete, due to its inability to express NOT. A gate (or set of gates) that is functionally complete can also be called a universal gate (or a universal set of gates). In a context of propositional logic, functionally complete sets of connectives are also called (''expressively'') ''adequate''.. (Defines "expressively adequate", shortened to "adequate set of connectives" in a section heading.) From the point of view of digital electronics, functional completeness means t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Matrix
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. An permutation matrix can represent a permutation of elements. Pre- multiplying an -row matrix by a permutation matrix , forming , results in permuting the rows of , while post-multiplying an -column matrix , forming , permutes the columns of . Every permutation matrix ''P'' is orthogonal, with its inverse equal to its transpose: P^=P^\mathsf. Indeed, permutation matrices can be characterized as the orthogonal matrices whose entries are all non-negative. The two permutation/matrix correspondences There are two natural one-to-one correspondences between permutations and permutation matrices, one of which works along the rows of the matrix, the other along its columns. Here is an example, starting with a permutation in two-line form at the upper left: :\begin \pi\colon\begin1&2&3&4\\3&2&4&1\e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XOR Gate
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive disjunction, exclusive or (\nleftrightarrow) from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both". An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a Inverter (logic gate), inverter (a NOT gate) which may be activated or deactivated by a switch. XOR can also be viewed as addition Modular arithmetic, modulo 2. As a result, XOR gates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Controlled NOT Gate
In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-''X'' gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states. Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. The gate is sometimes named after Richard Feynman who developed an early notation for quantum gate diagrams in 1986. The CNOT can be expressed in the Pauli basis as: : \mbox = e^= e^. Being both unitary and Hermitian, CNOT has the property e^=(\cos \theta)I+(i\sin \theta) U and U =e^=e^, and is involutory. The CNOT gate can be further decomposed as products of rotation operator gates and exactly one two qubit interaction gate, for example : \mbox =e^R_(-\pi/2)R_(-\pi/2)R_(-\pi/2)R_(\pi/2)R_(\pi/2). In general, any sing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
