Логикалық қақпалар және бульдік функциялар

Device performing a Boolean function

A logic gate is a device that performs a Boolean function, a logical operation performed on one or more 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). They can also be constructed using vacuum tubes, electromagnetic relays with relay logic, fluidic logic, pneumatic logic, optics, molecules, acoustics, or even mechanical or thermal elements. Logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic. Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory, all the way up through complete microprocessors, which may contain more than 100 million logic gates. Compound logic gates AND OR Invert (AOI) and OR AND Invert (OAI) are often employed in circuit design because their construction using MOSFETs is simpler and more efficient than the sum of the individual gates.

The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705), influenced by the ancient I Chings binary system. Leibniz established that using the binary system combined the principles of arithmetic and logic. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits. Early electro mechanical computers were constructed from switches and relay logic rather than the later innovations of vacuum tubes (thermionic valves) or transistors (from which later electronic computers were constructed). Ludwig Wittgenstein introduced a version of the 16 row truth table as proposition 5.101 of Tractatus Logico Philosophicus (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954 Nobel Prize in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935 to 1938). From 1934 to 1936, NEC engineer Akira Nakashima, Claude Shannon and Victor Shestakov introduced switching circuit theory in a series of papers showing that two valued Boolean algebra, which they discovered independently, can describe the operation of switching circuits. Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digital computers. Switching circuit theory became the foundation of digital circuit design, as it became widely known in the electrical engineering community during and after World War II, with theoretical rigor superseding the ad hoc methods that had prevailed previously. Both types were later combined and adapted into complementary MOS (CMOS) logic by Chih Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963.

Logic gates can also be used to hold a state, allowing data storage. A storage element can be constructed by connecting several gates in a "latch" circuit. Latching circuitry is used in static random access memory. More complicated designs that use clock signals and that change only on a rising or falling edge of the clock are called edge triggered "flip flops". Formally, a flip flop is called a bistable circuit, because it has two stable states which it can maintain indefinitely. The combination of multiple flip flops in parallel, to store a multiple bit value, is known as a register. When using any of these gate setups the overall system has memory; it is then called a sequential logic system since its output can be influenced by its previous state(s), i. e. by the sequence of input states. In contrast, the output from combinational logic is purely a combination of its present inputs, unaffected by the previous input and output states. These logic circuits are used in computer memory. They vary in performance, based on factors of speed, complexity, and reliability of storage, and many different types of designs are used based on the application.

A functionally complete logic system may be composed of relays, valves (vacuum tubes), or transistors. Electronic logic gates differ significantly from their relay and switch equivalents. They are much faster, consume much less power, and are much smaller (all by a factor of a million or more in most cases). Also, there is a fundamental structural difference. The switch circuit creates a continuous metallic path for current to flow (in either direction) between its input and its output. The semiconductor logic gate, on the other hand, acts as a high gain voltage amplifier, which sinks a tiny current at its input and produces a low impedance voltage at its output. It is not possible for current to flow between the output and the input of a semiconductor logic gate. For small scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 series by Texas Instruments, the CMOS 4000 series by RCA, and their more recent descendants. Increasingly, these fixed function logic gates are being replaced by programmable logic devices, which allow designers to pack many mixed logic gates into a single integrated circuit. The field programmable nature of programmable logic devices such as FPGAs has reduced the 'hard' property of hardware; it is now possible to change the logic design of a hardware system by reprogramming some of its components, thus allowing the features or function of a hardware implementation of a logic system to be changed. An important advantage of standardized integrated circuit logic families, such as the 7400 and 4000 families, is that they can be cascaded. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on. Systems with varying degrees of complexity can be built without great concern of the designer for the internal workings of the gates, provided the limitations of each integrated circuit are considered. The output of one gate can only drive a finite number of inputs to other gates, a number called the 'fan out limit'. Also, there is always a delay, called the 'propagation delay', from a change in input of a gate to the corresponding change in its output. When gates are cascaded, the total propagation delay is approximately the sum of the individual delays, an effect which can become a problem in high speed synchronous circuits. Additional delay can be caused when many inputs are connected to an output, due to the distributed capacitance of all the inputs and wiring and the finite amount of current that each output can provide.

A three state logic gate is a type of logic gate that can have three different outputs: high (H), low (L) and high impedance (Z). The high impedance state plays no role in the logic, which is strictly binary. These devices are used on buses of the CPU to allow multiple chips to send data. A group of three states driving a line with a suitable control circuit is basically equivalent to a multiplexer, which may be physically distributed over separate devices or plug in cards. In electronics, a high output would mean the output is sourcing current from the positive power terminal (positive voltage). A low output would mean the output is sinking current to the negative power terminal (zero voltage). High impedance would mean that the output is effectively disconnected from the circuit.

Non electronic implementations are varied, though few of them are used in practical applications. Many early electromechanical digital computers, such as the Harvard Mark I, were built from relay logic gates, using electro mechanical relays. Logic gates can be made using pneumatic devices, such as the Sorteberg relay or mechanical logic gates, including on a molecular scale. Various types of fundamental logic gates have been constructed using molecules (molecular logic gates), which are based on chemical inputs and spectroscopic outputs. Logic gates have been made out of DNA (see DNA nanotechnology) and used to create a computer called MAYA (see MAYA II). Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3 state logic for bus systems is not needed, and can be replaced by digital multiplexers, which can be built using only simple logic gates (such as NAND gates, NOR gates, or AND and OR gates).