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LOGIC GATES A logic gate takes one or more logic-level inputs and produces a single logic-level output. Because the output is also a logic level, an output of one logic gate can connect to the input of one or more other logic gates. With some types of logic gates, such as those with Open-collector outputs, two outputs may be wired together to produce what is known as a 'wired OR'. In electronic logic, a logic level is represented by a certain voltage (which depends on the type of electronic logic in use). Each logic gate requires power so that it can source and sink currents to achieve the correct output voltage. In logic circuit diagrams the power is not shown, but in a full electronic schematic, power connections are required. There are 7 positive logic gates and each gate has two laws or rules. TRUTH TABLE See Also: Truth table A truth table is a table that describes the behaviour of a logic gate. It lists the value of the output for every possible combination of the inputs and can be used to simplify the number of logic gates and level of nesting in an electronic circuit. In general the truth table does not lead to an efficient implementation; a minimization procedure, using Karnaugh Maps , the Quine–McCluskey Algorithm or a Heuristic Algorithm is required for reducing the circuit complexity. BACKGROUND The simplest form of electronic logic is Diode Logic . This allows AND and OR gates to be built, but not inverters, and so is an incomplete form of logic. To build a complete logic system, Valves (vacuum tubes) or Transistor s can be used. The simplest family of logic gates using bipolar transistors is called Resistor-transistor Logic , or RTL. Unlike diode logic gates, RTL gates can be cascaded indefinitely to produce more complex logic functions. These gates were used in early Integrated Circuit s. For higher speed, the resistors used in RTL were replaced by diodes, leading to Diode-transistor Logic , or DTL. It was then discovered that one transistor could do the job of two diodes in the space of one diode, so Transistor-transistor Logic , or TTL, was created. In some types of chip, to reduce size and power consumption still further, the bipolar transistors were replaced with complementary Field-effect Transistor s ( MOSFET s), resulting in complementary metal-oxide-semiconductor ( CMOS ) logic. For small-scale logic, designers now use prefabricated logic gates from Families Of Devices such as the TTL 7400 Series invented by Texas Instruments and the CMOS 4000 Series invented by RCA , and their more recent descendants. These devices usually contain transistors with multiple emitters, used to implement the AND function, which are not available as separate components. Increasingly, these fixed-function logic gates are being replaced by Programmable Logic Device s, which allow designers to pack a huge number of mixed logic gates into a single Integrated Circuit . The field-programmable nature of Programmable Logic Device s such as FPGA s has removed 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. 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. Another important advantage of standardised semiconductor logic gates, such as the 7400 and 4000 families, is that they are cascadable. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on ''ad infinitum'', enabling the construction of circuits of arbitrary complexity without requiring the designer to understand the internal workings of the gates. In practice, the output of one gate can only drive a finite number of inputs to other gates, a number called the ' Fanout limit', but this limit is rarely reached in the newer CMOS logic circuits, as compared to TTL circuits. 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 circuits. LOGIC GATES AND HARDWARE NAND and NOR logic gates are the two pillars of logic, in that all other types of Boolean logic gates (i.e., AND , OR , NOT , XOR , XNOR ) can be created from a suitable network of just NAND or just NOR gate(s). They can be built from relays or transistors, or any other technology that can create an inverter and a two-input AND or OR gate. Hence the NAND and NOR gates are called the universal gates. For an input of 2 variables, there are 16 possible boolean algebraic functions. These 16 functions are enumerated below, together with their outputs for each combination of inputs variables.
Logic gates are a vital part of many digital circuits, and as such, every kind is available as an IC. For examples, see the 4000 Series of CMOS logic chips or the 7400 TTL series. SYMBOLS There are two sets of symbols in common use, both now defined by EN 60617-12:1999 in the United Kingdom. The goal of IEEE Std 91-1984 was to provide a uniform method of describing the complex logic functions of digital circuits with schematic symbols. These functions were more complex than simple AND and OR gates. They could be medium scale circuits such as a 4-bit counter to a large scale circuits such as a microprocessor. The 1984 version did not include the "distinctive shape" symbols. {Link without Title} These were added to the 1991 supplement with this note: "The distinctive-shape symbol is, according to IEC Publication 617, Part 12, not preferred, but is not considered to be in contradiction to that standard." In the 1980s, schematics were the predominate method to design both circuit boards and custom ICs known as Gate Array s. Today custom ICs and the Field-programmable Gate Array are typically designed with Hardware Description Languages (HDL) such as Verilog or VHDL . The need for complex logic symbols has diminished and distinctive shape symbols are still the predominate style.
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