A logic gate is an arrangement of controlled switches used to calculate operations using Boolean logic in digital circuits. They are primarily implemented electronically (using diodes, transistors) but can also be constructed using electromagnetic relays, fluidics, optical or even mechanical elements.
Basic logic gates and mechanical equivalents Edit
While semiconductor electronic logic (see later) is preferred in most applications, relays and switches are still used in some industrial applications and for educational purposes. In this article, the various types of logic gates are illustrated with drawings of their relay-and-switch implementations, although the reader should remember that these are electrically different from the semiconductor equivalents that are discussed later.
Relay logic was historically important in industrial automation (see ladder logic and programmable logic controller). Since relay contacts conduct in both directions, complex logic designs must be checked for "sneak paths" that produce unintended logic paths.
Semiconductor logic gates are not conductive in both directions, as the input signal acts as a 'trigger' to allow current out of the output, rather than allowing current straight through from input to output. However, the following mechanical variations do show the basic principles of the gates without detailing the precise internal workings. For information about how modern semiconductors really work, see CMOS.
The three types of essential logic gate are the AND, the OR and the NOT gate. With these three, any conceivable boolean equation can be implemented. However, for convenience, the derived types NAND, NOR, XOR and XNOR are also used, which often use fewer circuit elements for a given equation than an implementation based solely on AND, OR and NOT would do. In fact the NAND has the lowest component count of any gate apart from NOT when implemented using modern semiconductor techniques, and since a NAND can implement both a NOT and, by application of De Morgan's Law, an OR function, this single type can effectively replace AND, OR and NOT, making it the only type of gate that is needed in a real system. Programmable logic arrays will very often contain nothing but NAND gates to simplify their internal design.
AND gates Edit
The first example is the AND gate, whose truth table is shown below, left. The Boolean AND function can be implemented with two switches, A and B, as shown below, right. If a power lead is connected to switch A, and a wire connects switches A and B, then both A and B have to be "on" in order for the output of the circuit to conduct electricity and provide power.
|A||B||A AND B|
OR gates Edit
Another important arrangement is the OR gate, whose truth table is shown below, left.
An OR gate can be constructed from two switches, arranged so that if either switch is "on", the output will also be "on". Note that the output will still be on even if both switches are on.
|A||B||A OR B|
NOT gates Edit
A simpler arrangement is the NOT gate, whose truth table is shown opposite.
This is a special switch that when pushed breaks the current when it is pressed. The normally-closed contact of a relay can be used for this purpose.
NAND and NOR gates Edit
Using NOT gates, also called inverters, allows us to make alternate versions of the AND and OR gates, by virtue of De Morgan's Law. Note that the layout of the switches in the two circuits is swapped when we turn the switches "backwards". Also note how the output of the first pair controls the operation of the NOT gate.
This may seem like an unnecessary complication, but in fact this is very useful. By removing the NOT gate from these alternate circuits, we create the so-called NAND (for NOT-AND) and NOR (for NOT-OR) gates.
|A||B||A NAND B|
|Type||Distinctive shape||Rectangular shape|
|In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is generally used in circuit diagrams to indicate an inverted input or output.|
|In practice, the cheapest gate to manufacture is usually the NAND gate. Additionally, Charles Peirce showed that NAND gates alone (as well as NOR gates alone) can be used to reproduce all the other logic gates.
Symbolically, a NAND gate can also be shown using the OR shape with bubbles on its inputs, and a NOR gate can be shown as an AND gate with bubbles on its inputs. This reflects the equivalency due to De Morgans law, but it also allows a diagram to be read more easily, or a circuit to be mapped onto available physical gates in packages easily, since any circuit node that has bubbles at both ends can be replaced by a simple bubble-less connection and a suitable change of gate. If the NAND is drawn as OR with input bubbles, and a NOR as AND with input bubbles, this gate substitution occurs automatically in the diagram (effectively, bubbles "cancel"). This is commonly seen in real logic diagrams - thus the reader must not get into the habit of associating the shapes exclusively as OR or AND shapes, but also take into account the bubbles at both inputs and outputs in order to determine the "true" logic function indicated.
Two more gates are the exclusive-OR or XOR function and its inverse, exclusive-NOR or XNOR. The two input Exclusive-OR is true only when the two input values are different, false if they are equal, regardless of the value. If there are more than two inputs, the gate generates a true at its output if the number of trues’s at its input is odd (). In practice, these gates are built from combinations of simpler logic gates.
Storage of bits Edit
Related to the concept of logic gates (and also built from them) is the idea of storing a bit of information. The gates discussed up to here cannot store a value: when the inputs change, the outputs immediately react. It is possible to make a storage element either through a capacitor (which stores charge due to its physical properties) or by feedback. Connecting the output of a gate to the input causes it to be put through the logic again, and choosing the feedback correctly allows it to be preserved or modified through the use of other inputs. A set of gates arranged in this fashion is known as a "latch", and more complicated designs that utilise clocks (signals that oscillate with a known period) and change only on the rising edge are called edge-triggered "flip-flops". The combination of multiple flip-flops in parallel, to store a multiple-bit value, is known as a register.
These registers or capacitor-based circuits are known as 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.
Three-state logic gates Edit
Three-state, or 3-state, logic gates are a form of electronic logic gate in which the output has three possible states: high (H), low (L) and high-impedance (Z). The Z state exists merely to help the circuit designer and, unlike the H and L states, carries no information. This feature is used in circuits that have two or more logic outputs connected to a single logic input. A control circuit enables one output at a time depending on the logic function that is required, the other outputs being held in the Z state (also called 'disabled').
'Tri-state', a widely-used synonym of 'three-state', is a trademark of the National Semiconductor Corporation.
Logic circuits include such devices as multiplexers, registers, ALUs, and computer memory, all the way up through complete microprocessors which can contain more than a million gates. In practice, the gates are made from field effect transistors (FETs), particularly metal-oxide-semiconductor FETs (MOSFETs).
History and development Edit
The earliest logic gates were made mechanically. Charles Babbage[], around 1837, devised the Analytical Engine. His logic gates relied on mechanical gearing to perform operations. Electromagnetic relays were later used for logic gates. In 1891, Almon Strowger patented a device containing a logic gate switch circuit (Template:US patent). Strowger's patent was not in widespread use until the 1920s. Starting in 1898, Nikola Tesla []filed for patents of devices containing logic gate circuits (see List of Tesla patents). Eventually, vacuum tubes replaced relays for logic operations. Lee De Forest's modification, in 1907, of the Fleming valve can be used as AND logic gate. Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switching circuits in 1937. 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.
See also Edit
- Digital circuit
- Karnaugh map[]
- List of Boolean algebra topics[]
- Logic families ]
- Race hazard[]
- Venn diagram[]
- Symbols for logic gates. Twenty First Century Books, Breckenridge, CO.
- Tesla's invention of the AND logic gate. Twenty First Century Books, Breckenridge, CO.
- Wireless Remote Control and the Electronic Computer Logic Gate. Twenty First Century Books, Breckenridge, CO.
- Anderson, Leland I., "Nikola Tesla — Guided Weapons & Computer Technology". ISBN 0-9636012-5-3
- Bigelow, Ken, "How logic gates work internally (for several logic families)", play-hookey.com.
- C. E. Shannon, "A symbolic analysis of relay and switching circuits," Transactions American Institute of Electrical Engineers, vol. 57, pp. 713-723, March 1938.
- The International Electrotechnical Commission IEC[] symbols are defined in IEC 60617-12 (1997-12), Graphical symbols for diagrams - Part 12: Binary logic elements
Further reading Edit
- Bostock, Geoff, "Programmable logic devices : technology and applications". New York, McGraw-Hill, c1988. ISBN 0070066116
- Brown, Stephen D. et. al., "Field-programmable gate arrays". Boston, Kluwer Academic Publishers, c1992. The Kluwer international series in engineering and computer science. ISBN 0792392485
- Awschalom, D., D. Loss, and N. Samarth, "Semiconductor spintronics and quantum computation". Berlin, Springer, c2002. ISBN 3540421769