Fredkin gate

Fredkin gate

The Fredkin gate is computational circuit suitable for reversible computing, invented by Ed Fredkin. It is "universal", which means that any logical or arithmetic operation can be constructed entirely of Fredkin gates.

The basic Fredkin gate is a "controlled swap gate" that maps three inputs ("C", "I"1, "I"2) onto three outputs ("C", "O"1, "O"2). The "C" input is mapped directly to the "C" output. If "C" = 0, no swap is performed; "I"1 maps to "O"1, and "I"2 maps to "O"2. Otherwise, the two outputs are swapped so that "I"1 maps to "O"2, and "I"2 maps to "O"1. It is easy to see that this circuit is reversible, i.e., "undoes itself" when run backwards. A generalized "n"×"n" Fredkin gate passes its first "n"-2 inputs unchanged to the corresponding outputs, and swaps its last two outputs if and only if the first "n"-2 inputs are all 1.

The Fredkin gate is the reversible 3-bit gate that swaps the last two bits if the first bit is 1. Its truth table is shown to the right.

It has the useful property that the numbers of 0s and 1s are conserved throughout, which in the billiard ball model means the same number of balls are output as input. This corresponds nicely to the conservation of mass in physics, and helps to show that the model is not wasteful.

Logic function with XOR and AND gates

"O"1 = "I"1 XOR "S"

"O"2 = "I"2 XOR "S"

with "S" = ("I"1 XOR "I"2) AND "C"

Example

Here is a diagram of a 3-bit adder implemented using Fredkin gates. The three inputs are A, B and C, supplemented by the constant T and F. In the diagram, the leftmost input (before the colon) swaps the two rightmost inputs if it is true.

See also

*Toffoli Gate, which is a "controlled-controlled-NOT gate".


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Fredkin Gate — Das Fredkin Gate ist eine von Edward Fredkin erfundene Schaltung, die für reversibles Computing verwendet wird. Der Input wie auch der Output bestehen aus 3 Bits. Ist das erste Bit 1, werden die anderen beiden miteinander vertauscht. Wenn nicht… …   Deutsch Wikipedia

  • Fredkin-Gate — Eingänge Ausgänge C I1 I2 C O1 O2  0   0   0   0   0   0  0 0 1 0 0 1 …   Deutsch Wikipedia

  • Fredkin — bezeichnet Edward Fredkin (*1934), US amerikanischer Physiker das von ihm erfundene Fredkin Gate, eine Computer Schaltung Diese Seite ist eine Begriffsklärung zur Unterscheidung mehrerer mit demselben Wort bezeichneter Begri …   Deutsch Wikipedia

  • Toffoli gate — In computer science, the Toffoli gate, invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any reversible circuit can be constructed from Toffoli gates. It is also known as the controlled controlled not gate, which …   Wikipedia

  • Edward Fredkin — (born 1934) is an early pioneer of digital physics (in recent work he uses the term digital philosophy (DP)). His main contributions include his work on reversible computing and cellular automata. While Konrad Zuse s book Calculating Space (1969) …   Wikipedia

  • Edward Fredkin — (* 1934) ist ein früher Pionier der Digitalen Physik (in letzter Zeit verwendete er den Begriff Digitale Philosophie). Die Hauptbeiträge seiner Arbeit sind im Bereich Reversible Computing und Zellulärer Automat. Während Konrad Zuses Buch… …   Deutsch Wikipedia

  • Reversible Computing/3 input universal logic gates — Logic gates are used to build computer chips. Reversible logic gates are of interest because they could in principle generate useful results for less heat generated (Landauer 1961). The nand gate is universal among irreversible logic gates, in… …   Wikipedia

  • Quantum digital signature — A Quantum Digital Signature (QDS) refers to the quantum mechanical equivalent of either a classical digital signature or, more generally, a handwritten signature on a paper document. Like a handwritten signature, a digital signature is used to… …   Wikipedia

  • Liste der Quantengatter — Dies ist eine Auflistung verschiedener Quantengatter und deren Funktion. Inhaltsverzeichnis 1 Quantengatter mit einem Eingang 2 Quantengatter mit zwei Eingängen 3 Quantengatter mit drei Eingängen …   Deutsch Wikipedia

  • Quantum circuit — In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of reversible transformations on a quantum mechanical analog of an n bit register. This analogous structure is referred to as …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”