Switching function

This article places from the start within the framework of the traditional Logique.

There exist two great types of switching functions :

• switching functions “combinative”, bases of boolean algebra, which only result from the combinative analysis of the variations of the sizes of entries.
• switching functions “sequential” or Rocker S, which results from the association of several switching functions “combinative” and which suppose the existence of a clock which gives time: in this case, the values of exits depend not only on the values of entry, but also on the values of exit at the previous moment.

The combinative switching functions directly resulting from mathematics (Boolean algebra) are the basic tools of the numerical electronic thus of the automatism and the Informatique. They are used in electronics in the form of logical doors .

• These electronic doors are built starting from several Transistor S connected to each other. In other applications, one can find doors logical containing relay, of fluids or of optical or mechanical elements
• According to the modeling used, one will take into account the time lags or not calculation.

History

Wheel toothed with the molecule

The first switching functions were fulfilled in a mechanical way. Charles Babbage, about 1837, designed the “analytical machine”, assembly of doors connected to wheels toothed to carry out logical operations. Thereafter, the logical operations were carried out thanks to electromagnetic relays.

In 1891, Almon Strowger deposited a patent for an apparatus containing a switch based on a logical door (). Its patent was hardly exploited until in the years 1920. As from 1898, Nikola Tesla deposited a series of patents concerning of the apparatuses based on circuits with logical doors. Finally, the vacuum tubes replaced the relays for the logical operations. In 1907, Lee De Forest modified one of these tubes and used it as a logical door AND. Claude E. Shannon introduced the use of the Boolean algebra into the design of circuits in 1937. Walther Bothe, inventor of the coincidence circuit, accepted the Nobel Prize of physics in 1954, for the creation of the first logical AND electronic door modern in 1924. Research tasks are currently undertaken for the generation of molecular logical doors.

Logical doors with transistors

The simplest form of electronic logic is logic with Diode S. That allows the manufacture of doors And OR, but not of doors NOT what leads to an incomplete logic. To create a complete logical system, it is necessary to use lamps or Transistor S.

The simplest family of logical doors using of the bipolar transistors is called resistance-transistor or RTL ( resistor-transistor logic ). Contrary to the doors with diodes, doors RTL can be put in cascade indefinitely to produce complex switching functions. To decrease the time lag, the resistances used by doors RTL were replaced by diodes, which gave rise to the logical doors diode-transistor or DTL ( diode-transistor logic ). It was discovered then that a transistor could do the work of two diodes by replacing only one, which led to the creation of logical doors transistor-transistor or TTL ( transistor-transistor logic ). In certain types of circuits, the bipolar transistors were replaced by field-effect transistors (MOSFET) what gave rise to logic CMOS.

The logical originators of circuits currently use prefabricated integrated circuits, in particular in TTL, the series 7400 of Texas Instruments, and in CMOS, series 4000 of RCA, like their more recent derivatives. The majority of these circuits contain transistors with several transmitters, used to implement the function AND, and which are not available separately. More and more, these fixed logical circuits are replaced by programmable circuits, which make it possible to the originators to integrate a great number of various logical doors in only one Integrated circuit. The programmable nature of these circuits, among which FPGA, removed with the hardware its aspect " dur" : it is from now on possible to change the switching functions of a system by reprogramming some of its components, which makes it possible to modify the characteristics of a logical circuit hardware.

The electronic logical doors differ significantly from their equivalents with relay and contacts. They are much faster, less greedy and much smaller (at least a million times in the majority of the cases). Moreover, there is a basic difference in the structure. The circuits with contacts create a continuous way, in which the current can circulate in the two directions between the entry and the exit. The logical door with semiconductors, on the contrary, acts like powerful a Amplificateur of tension, which receives a low current in entry and produces a basic tension impedance output. The current cannot circulate between the exit and the entry of a door with semiconductors.

Another great advantage of the standardized logical circuits is that they can be put in cascade. In other words, the exit of a door can be connected to the entries of one or more doors, and thus of following the infinite one, which makes it possible to build circuits of an unspecified complexity without needing to know the inner working of the doors. In practice, the exit of a door can be connected only to one finished number of entries, but this limit is seldom reached in the new circuits CMOS compared with circuits TTL. There exists also a time named time travel between the modification of an entry and the corresponding modification at exit. In doors in cascade, the total travel time is about equal to the sum of the individual travel times, which can pose problem in the circuits at high speed.

Classification

Logical levels

- In Boolean algebra, a data, that it is in entry or exit, has only two possible levels. According to the applications, these two levels can bear different names: go/stop, high/low, one (1)/zero (0), false, positive/negative, positive truth//no one, open circuit/closed circuit, potential difference/not of difference, yes/not. - - In the case of electronic circuits, the two levels are represented by two levels of tension, “high” and “low”. Each type of circuit has its own levels of tension, to make sure of connectivity between the entries and exits of the circuits. Usually, two quite distinct levels (not being likely to overlap) are defined; the difference between the two levels varies between 0,7 volts and 28 volts (this last in the case of relays). - - To harmonize the notation, these two levels will be noted here 1 and 0.

Switching functions

The doors can be classified according to their number of entries:

• “doors” without entry: TRUTH, FORGERY;
• doors at a entry: NOT ( NOT ), YES ;
• doors at two entries: AND ( AND ), NON-ET ( NAND ), OR ( GOLD ), exclusive NON-OU ( NOR ), OR ( XOR ), Coincidence exclusive known as also NON-OU or equivalence ( XNOR ), Implication;
• Starting from three entries, the number of functions starts to be subject to the influence of the combinative Explosion. One notes however the existence of: AND, OR, etc with more than two entries.

It is possible to reconstitute the functions NOT, AND and OR by using only either the function NON-ET, or the function NON-OU. One evokes this characteristic under the concept of universality of the operators NON-OU and NON-ET (cf the binary connector of incompatibility, also called bars Sheffer).

When two compatible logical doors are associated, one can connect two entries together, or an entry on an exit. One should not in no case to connect two different exits because they can produce different data; in the case of electronic doors, that would be equivalent to a Court-circuit.

Representation

To define each switching function, we will give several representations:

• an electric representation: diagram developed with contacts;

• an algebraic representation: equation;
• an arithmetic representation: Truth table;
• a temporal representation: chronogram;
• a chart: logical symbol.

In the case of electronic doors, a logical level is represented by a definite voltage (according to the type of component used). Each logical door must thus be fed to deliver the suitable output voltage. In the representation in logical symbols, this food is not represented, but it owes the being in a complete electronic diagram.

The representation of a combinative system including several switching functions can also be done thanks to a Schéma with contact, an equation, a Truth table and a graphic diagram. In this last case one will speak about a logigramme.

Chart

Two whole of symbols is used to represent the switching functions; both are defined by the standard ANSI/IEEE 91-1984 and its supplement 91a-1991. The representation by “distinctive symbols”, based on traditional schematizations, is used for the simple diagrams and is easier to trace with the hand. It is sometimes described as “soldier”, which reflects his origins, if not his current use.

The “rectangular” representation is based on the standard CEI 60617-12; all the doors are represented there with rectangular edges and a symbol, which allows the representation of a greater number of the types of circuits. This system was taken again by other standards like IN 60617-12: 1999 in Europe and BS IN 60617-12: 1999 in the United Kingdom.

|- | OR | | | $\backslash \; textstyle\; has\; +\; B$ | |- | NOT | | | $\backslash \; overline\; \{has\}$ | |- | colspan=" 5" |In electronics, a door NOT is more commonly called reverser . The circle used on the representation is called “bubble”, and one generally uses it in the diagrams to show that an entry or an exit is reversed. |- | NON-ET (NAND) | | | $\backslash \; overline\; \{has\; \backslash \; cdot\; B\}$ | |- | NON-OU (NOR) | | | $\backslash \; overline\; \{has\; +\; B\}$ | |- | OR exclusive (XOR) | | | $A\; \backslash oplus\; B$ | |- | exclusive or Exclusive-OR NON-OU complémenté (XNOR) | | | $\backslash \; overline\; \{has\; \backslash \; oplus\; B\}$ | |} A door NON-ET (NAND) can also be represented by using the symbol OR with bubbles (reversers) on the entries, and a door NON-OU (NOR) can be represented by a symbol AND with bubbles on the entries. That reflects the laws of equivalence of Morgan; that also makes it possible to make a diagram more readable, or to easily manufacture a circuit with prefabricated doors, because a circuit which has bubbles on the two sides can be replaced by a circuit not-reversed by changing the door. If a door NON-ET is represented by one OR with reversed entries, or that a NON-OU is represented by one AND with reversed entries, the replacement is done automatically in the diagram (the bubbles “are cancelled”). That is current in the real logical diagrams - so that the reader does not have to be accustomed to associate the symbols with the doors OR and automatically, but must also take into account the reversers to determine the good function represented. The reversed entries are particularly useful in the case of active signals “at the low state”.

The two other doors frequently met are the function OR exclusive and its reverse. One OR exclusive at two entries returns one 1 only when the two entries are different, and one 0 when they are equal, whatever their value. If there is more than two entries, the door returns 1 if the number of entries equal to 1 is odd (). In practice, these doors are often carried out starting from simpler combinations of logical doors.

Other switching functions

Logical doors in 3 states

Logical the doors known as “in three states” have an exit which can take three different states: high, low and high impedance or Z . The state of high impedance does not play any part in the logic itself which remains binary; it is equivalent in fact to an open circuit, or a “absence” of exit. These doors are used in the electronic buses for the sending of data; a group of doors in three states controlled by an earth phantom circuit is equivalent to a Multiplexeur which can be distributed physically on several electronic apparatuses or several charts.

Storage units

In addition to the concept of logical doors, arises the difficulty of the storage of a Bit of information. The logical doors presented higher do not store data: when an entry changes, the exit reacts immediately (at the travel time near). It is possible to create elements of storage either with Condensateur S, or by using the feedback . While connecting the exit of a door to his entry, one returns the exit in the logical circuit; it can thus be preserved or modified by using the other entries. By connecting doors in this manner, one creates a bolt ( latch in English). Other circuits a little more complex use clock signals (signals which oscillate at a known frequency) and change when the clock signal passes to 1; they are called Bascule S ( flip-failures in English). By combining several rockers in parallel to store a value of several bits, one creates a register.

The registers and other circuits of storage are gathered under the term of “electronic memories”. Their performances vary in terms speed, complexity and reliability of the memory. Their types can be very different according to the applications.

Other units

The logical circuits can also contain elements like Multiplexeur S, arithmetic logic units (in English: Arithmetic and Logic Links or ALUMINUM ) and of the memories. The assembly of such elements constitutes Microprocesseur S which can contain more than 100 million logical doors. The components of microprocessors are containing field-effect transistors, in particular of MOSFET.

Bonds

References

• Symbols for logic spoil . Twenty First Century Books, Breckenridge, CO.

• Tesla' S invention off and logic spoils . Twenty First Century Books, Breckenridge, CO.
• Wireless Remote Control and the Electronic Computer Logic logic elements
• LEGO Logic Spoil . goldfish.org .uk, 2005.

See too

• Fan-out

• Table of Karnaugh

Simple: Logic spoils

Random links:

Chen Boda | Gaëtane Prouvost | Daily Star (Bangladesh) | Ground fractal | Law of the controversy of Bendford

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