Logic gate

A logic gate or gates only (English gate), is an electronic device for implementing a Boolean function which can process the input signals to output signals. The input signals are converted by implementing logical operators such as AND, OR or NOT, to form a single logical result and mapped by the output signals. For the implementation it is, however, different ways.

Electronic logic gates are usually implemented together with diodes and transistors. The signals are here, different voltages are applied to one or more inputs of the gate line. The voltages represent the logic states, and are commonly referred to as "0" or " 1" which also allows an interpretation as numbers. Results as implemented gates can be used as inputs for other gates, making it easy to create versatile circuits again.

History

Mathematically exactly the binary system was first described by Gottfried Wilhelm Leibniz (published in 1705 ), where Leibniz also explained how the principles of arithmetic and logic can be combined using this system.

The first logic gate were still realized mechanically. 1837 was designed by the English inventor Charles Babbage Analytical Engine with a calculating machine, which is an important step in the history of the computer today. His " logic gates " were working on the basis of mechanical reactions, while electromagnetic relay already been used later.

1891 reported the American Almon Strowger a " unit containing a logic gate switch circuit " for a patent, which, however, until the 1920s could not be established. 1898 began the inventor Nikola Tesla with the archiving and refinement of such units and put the use of electron tubes instead of relays through. Lee De Forest changed the circuit design of Fleming 's electron tube in the year 1907, so that it could be used as an AND gate.

The Austrian philosopher Ludwig Wittgenstein introduced in 1921 in the theorem 5101 his treatise Tractatus Logico-Philosophicus, the first truth table, but without calling it that. Walther Bothe, inventor of the coincidence circuit, received the Nobel Prize (1954 ) for part of the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 ( 1935-1938 ).

The American mathematician Claude Elwood Shannon founded in 1937 Wittgenstein's considerations with the introduction of Boolean algebra in the analysis and design of circuit circuits. Current research projects focus on molecular logic gates.

Truth table

The possible output states of a logic gate may be displayed in response to the input states in a truth table. It lists all the possible combinations of the input signals and provides the corresponding outputs. From this one can relatively easily deduce logical formulas. The individual lines with the same initial values ​​are in the disjunctive normal form ( 1 as a result ) with logical " or" and the individual inputs with logic " and" linked. In the conjunctive normal form ( 0 as a result ), it is vice versa. To obtain a compact formula, one can use a chart CT.

KV- chart

The Karnaugh - Veitch - Diagram is an easy way to make from the disjunctive or conjunctive normal form, the most compact, logical formula. Through meaningful grouping of zeros or ones and "favorable" interpretation of the redundant fields ( "empty" fields that have no influence on the function), these compact shape.

Types of logic gates and symbols

Earlier, the German symbols (right column) were common on the European continent; were in the English language and the American symbols ( middle column) common. The IEC symbols are encountered internationally on limited acceptance and are ignored consistently in American literature.

Background

Gates as TTL, CMOS or BiCMOS devices in the form of individual integrated circuits available for a few cents. They form the core of microprocessors, or can be programmed in thousands in software in FPGA or PLD ICs. Of particular importance here are the NAND and NOR gates, because you can reduce all binary functions according to Quine / McCluskey on the three basic elements of AND, OR and NOT. Again, can be represented using NAND gates OR, and NOT, and AND and NOT from NOR gates. One can thus realize any logic circuit solely by NAND or NOR blocks.

Most popular Date for the development of automation and computer technology, the quad NAND gate obtained, therefore, in the 1970s, 7400 (TTL) and 4011 ( CMOS), as well as the quad NOR gate 7402 (TTL) and 4001 ( CMOS).

The number of gate equivalents is used as a measure of the complexity of a logic circuit.

The first integrated logic gate goes back to Jack Kilby in 1958 and consisted of about ten components. Ten years later made ​​Texas Instruments TTL Circuits ( Series 7400 ) in large series. She quickly became the basis of industrial automation.

Logic gates are designated circuit symbols. The following are the types of logic gates, XOR gates, NOR gates, NAND gates, XNOR gates, AND gates, OR gates and NOT gate. All other arbitrarily complex logical functions are generated by linking several logic gates. Several logic gates can be connected together to form a flip-flop, latch, or multiplexer, for several flip-flops, you can create data storage and meter, and several of these circuits you can put together a microprocessor.