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92-618: Conventional analog control of model railways works by varying the track power and any locomotive on the track will respond by running at a speed roughly proportional to the power. For multiple trains, sidings must have a switch to isolate trains standing there and leave the track dead. For multiple controllers, the layout must be divided into sections isolated from each other and each with its own controller and current supply. All accessories such as signals and turnouts require individual switches and cables, making wiring very complex. With analog systems, fine control of locomotives requires knowledge of

184-435: A binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits. Solenoid A solenoid ( / ˈ s oʊ l ə n ɔɪ d / ) is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field . The coil can produce a uniform magnetic field in a volume of space when an electric current

276-409: A byte or word , is referred to, it is usually specified by a number from 0 upwards corresponding to its position within the byte or word. However, 0 can refer to either the most or least significant bit depending on the context. Similar to torque and energy in physics; information-theoretic information and data storage size have the same dimensionality of units of measurement , but there

368-439: A ferromagnetic core, such as iron , increases the magnitude of the magnetic flux density in the solenoid and raises the effective permeability of the magnetic path. This is expressed by the formula where μ eff is the effective or apparent permeability of the core. The effective permeability is a function of the geometric properties of the core and its relative permeability. The terms relative permeability (a property of just

460-509: A unit of information , the bit is also known as a shannon , named after Claude E. Shannon . The symbol for the binary digit is either "bit", per the IEC 80000-13 :2008 standard, or the lowercase character "b", per the IEEE 1541-2002 standard. Use of the latter may create confusion with the capital "B" which is the international standard symbol for the byte. The encoding of data by discrete bits

552-488: A 32 bit architecture, compared to 8 bits of the previous generation. The mLD/mSD generation is faster, has more memory, including 64 Mb memory reserved for sound data, as well as improved sound processing. With 4096 speed steps for the motor, and self calibration, motor characteristics, especially at low speeds, are improved. Along with these decoders, Märklin released the 60971 mDP/3, (Märklin Dekoder Programmer),

644-482: A Bell Labs memo on 9 January 1947 in which he contracted "binary information digit" to simply "bit". A bit can be stored by a digital device or other physical system that exists in either of two possible distinct states . These may be the two stable states of a flip-flop , two positions of an electrical switch , two distinct voltage or current levels allowed by a circuit , two distinct levels of light intensity , two directions of magnetization or polarization ,

736-563: A USB device which allows for easy programming of parameters of the mLD/mSD decoders as well as customizing sounds and images. The firmware of the decoders can be updated. The related software, mDT (Märklin Dekoder Tool) is adapted for Windows platforms. The decoder upgrade kits are not suitable for motors with older field-wound coils. Locomotives with these motors must be converted with the appropriate motor retrofit kits, item numbers 60941, 60943, or 60944. The decoders can be operated with

828-429: A bit was represented by the polarity of magnetization of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other. The same principle was later used in the magnetic bubble memory developed in the 1980s, and is still found in various magnetic strip items such as metro tickets and some credit cards . In modern semiconductor memory , such as dynamic random-access memory ,

920-399: A model. The Central Station 60212 had two locomotive controllers built in and a large monochrome LCD screen with graphical display and descriptive names for locomotives. The controller stored a database of pre-mfx digital locomotives with their functions so that they may be easily set up (mfx decoders send their own available functions to the controller). The new protocol was incompatible with

1012-436: A separate 6035 locomotive Control 80 with speed controller, keypad for decoder address, Function / Off buttons, and Start / Stop buttons to switch track power. The red Stop button was provided as an emergency stop to immediately halt all trains. A two digit display showed the selected locomotive address (01 - 80). Solenoid devices, such as turnouts , were controlled by the 6040 Keyboard. Up to ten controllers could be added to

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1104-435: A single locomotive controller, small LCD screen, and 9 function buttons. This unit could be used on its own as a low cost digital controller with up to ten locomotives in its own database or plugged into a Central Station as an additional controller. In 2008 Märklin announced a new second generation Central Station 60213 with colour display and enhanced features, this unit developed by a different contractor. The Central Station

1196-426: A solenoid bent into a horseshoe shape (similarly to an arc spring ). Solenoids provide magnetic focusing of electrons in vacuums, notably in television camera tubes such as vidicons and image orthicons. Electrons take helical paths within the magnetic field. These solenoids, focus coils, surround nearly the whole length of the tube. An infinite solenoid has infinite length but finite diameter. "Continuous" means that

1288-404: A time in serial transmission , and by a multiple number of bits in parallel transmission . A bitwise operation optionally processes bits one at a time. Data transfer rates are usually measured in decimal SI multiples of the unit bit per second (bit/s), such as kbit/s. In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's Analytical Engine , a bit

1380-437: A wire with the thumb pointing in the direction of the current, the curl of the fingers shows how the field behaves. Since we are dealing with a long solenoid, all of the components of the magnetic field not pointing upwards cancel out by symmetry. Outside, a similar cancellation occurs, and the field is only pointing downwards. Now consider the imaginary loop c that is located inside the solenoid. By Ampère's law , we know that

1472-416: Is a derivation of the magnetic flux density around a solenoid that is long enough so that fringe effects can be ignored. In Figure 1, we immediately know that the flux density vector points in the positive z direction inside the solenoid, and in the negative z direction outside the solenoid. We confirm this by applying the right hand grip rule for the field around a wire. If we wrap our right hand around

1564-486: Is in general no meaning to adding, subtracting or otherwise combining the units mathematically, although one may act as a bound on the other. Units of information used in information theory include the shannon (Sh), the natural unit of information (nat) and the hartley (Hart). One shannon is the maximum amount of information needed to specify the state of one bit of storage. These are related by 1 Sh ≈ 0.693 nat ≈ 0.301 Hart. Some authors also define

1656-405: Is independent of current. Similar analysis applies to a solenoid with a magnetic core, but only if the length of the coil is much greater than the product of the relative permeability of the magnetic core and the diameter. That limits the simple analysis to low-permeability cores, or extremely long thin solenoids. The presence of a core can be taken into account in the above equations by replacing

1748-554: Is more compressed—the same bucket can hold more. For example, it is estimated that the combined technological capacity of the world to store information provides 1,300 exabytes of hardware digits. However, when this storage space is filled and the corresponding content is optimally compressed, this only represents 295 exabytes of information. When optimally compressed, the resulting carrying capacity approaches Shannon information or information entropy . Certain bitwise computer processor instructions (such as bit set ) operate at

1840-496: Is neither DC nor AC ). Every locomotive must be fitted with a decoder circuit which will interpret instructions and individually control the motor. Each decoder has its own address, instructions sent from the controller have a corresponding address so that while every active decoder will receive the instructions only the addressed decoder will respond. Once a locomotive is running it will continue and so even with one controller several trains can be running. Many locomotives may be on

1932-495: Is passed through it. André-Marie Ampère coined the term solenoid in 1823, having conceived of the device in 1820. The French term originally created by Ampère is solénoïde , which is a French transliteration of the Greek word σωληνοειδὴς which means tubular . The helical coil of a solenoid does not necessarily need to revolve around a straight-line axis; for example, William Sturgeon 's electromagnet of 1824 consisted of

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2024-476: Is the magnetic constant , N {\displaystyle N} the number of turns, I {\displaystyle I} the current and l {\displaystyle l} the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density B {\displaystyle B} by the cross-section area A {\displaystyle A} : Combining this with

2116-416: Is the magnetic constant , N {\displaystyle N} the number of turns, and I {\displaystyle I} the current. From this we get This equation is valid for a solenoid in free space, which means the permeability of the magnetic path is the same as permeability of free space, μ 0 . If the solenoid is immersed in a material with relative permeability μ r , then

2208-424: Is the most basic unit of information in computing and digital communication . The name is a portmanteau of binary digit . The bit represents a logical state with one of two possible values . These values are most commonly represented as either " 1 " or " 0 " , but other representations such as true / false , yes / no , on / off , or + / − are also widely used. The relation between these values and

2300-458: The line integral of B (the magnetic flux density vector) around this loop is zero, since it encloses no electrical currents (it can be also assumed that the circuital electric field passing through the loop is constant under such conditions: a constant or constantly changing current through the solenoid). We have shown above that the field is pointing upwards inside the solenoid, so the horizontal portions of loop c do not contribute anything to

2392-1293: The vector potential , which for a finite solenoid with radius R and length l in cylindrical coordinates ( ρ , ϕ , z ) {\displaystyle (\rho ,\phi ,z)} is A ϕ = μ 0 I π R l [ ζ ( R + ρ ) 2 + ζ 2 ( m + n − m n m n K ( m ) − 1 m E ( m ) + n − 1 n Π ( n , m ) ) ] ζ − ζ + , {\displaystyle A_{\phi }={\frac {\mu _{0}I}{\pi }}{\frac {R}{l}}\left[{\frac {\zeta }{\sqrt {(R+\rho )^{2}+\zeta ^{2}}}}\left({\frac {m+n-mn}{mn}}K(m)-{\frac {1}{m}}E(m)+{\frac {n-1}{n}}\Pi (n,m)\right)\right]_{\zeta _{-}}^{\zeta _{+}},} Where: Here, K ( m ) {\displaystyle K(m)} , E ( m ) {\displaystyle E(m)} , and Π ( n , m ) {\displaystyle \Pi (n,m)} are complete elliptic integrals of

2484-410: The yottabit (Ybit). When the information capacity of a storage system or a communication channel is presented in bits or bits per second , this often refers to binary digits, which is a computer hardware capacity to store binary data ( 0 or 1 , up or down, current or not, etc.). Information capacity of a storage system is only an upper bound to the quantity of information stored therein. If

2576-449: The 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a mercury delay line , charges stored on the inside surface of a cathode-ray tube , or opaque spots printed on glass discs by photolithographic techniques. In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory , magnetic tapes , drums , and disks , where

2668-436: The 1950s Märklin models had four digit numbers, the first two being the group and the last two the individual model. Locomotives fitted with the original c80 digital decoders were numbered 36xx (36 followed by two digits e.g. 3615) and the first models fitted with c90 decoders 37xx (e.g. 3702). In 1997 Märklin had to expand the numbering to five digits 37xxx and a few new c90 equipped models were numbered with five digits before

2760-561: The 1991 introduction of c90 (6090) decoders with regulation and a 5-pole DC motor brought the system to maturity. Decoders had miniature switches ( DIP switches ) to set the address and c90 decoders had two potentiometers to adjust braking / acceleration delay ("inertia") and maximum speed, requiring the use of tools to open the model and make any changes to settings. Signals, turnouts, uncouplers, lights, and other static accessories may also be fitted with decoders which have their own address range for up to 256 switched devices. Depending on

2852-436: The 5 switched functions to control train lighting and other additional features. They may also be fitted to locomotives lacking the additional switched functions (i.e. c90 equipped locomotives). Function decoders require their own address from the 80 addresses available for locomotives (the address can be shared with another decoder lacking additional functions). Märklin had offered some special models with additional functions for

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2944-532: The 6020, 6021, Mobile Station, and Central Station controllers and can be programmed with the protocols MM, mfx, and DCC The retrofit kits come in 3 different formats. All the mSD3 kits come with 2 speaker options, small and large, except for 60978 and 60979, including one speaker. For upgrades to fixed circuit board with a 21 pin decoder interface. For upgrades of 36xxx series Märklin/Trix fixed circuit board locomotives with LED lights. For use with existing 8 pin connector in locomotive Bit The bit

3036-406: The 6043 Memory, which was used for switching predefined routes each with multiple turnouts & signals. The 6043 could save up to 24 different routes, which each route containing up to 20 individual device commands. The 20th command in one route memory could be used to link to another route button, so there could be a large number of individual commands enacted by pressing one button. In addition,

3128-500: The 6088 s88 Feedback Module could be used in conjunction with the 6043. The s88 would receive input signals from external buttons or magnetic reed switches and then start a command string in the 6043 Memory. So, an approaching train could set up its own route, as an example. Another accessory was the 6050 computer Interface which let the system be computer controlled, allowing for fully automated train control. The first c80 (6080) decoders did not have motor regulation (speed control) and

3220-615: The Function / Off buttons and c80 Digital models running on DELTA had Function permanently on which affected any such models equipped with TELEX remote couplers. c90 models running on DELTA had Function permanently off. In 2004 the completely new Märklin Systems digital control was unveiled. A new two way protocol can control up to 65,000 digital devices, each locomotive can have up to 128 speed steps and 16 functions. Developed by ESU with all components initially made by them for Märklin, later

3312-409: The ambiguity of relying on the underlying hardware design, the unit octet was defined to explicitly denote a sequence of eight bits. Computers usually manipulate bits in groups of a fixed size, conventionally named " words ". Like the byte, the number of bits in a word also varies with the hardware design, and is typically between 8 and 80 bits, or even more in some specialized computers. In

3404-424: The average. This principle is the basis of data compression technology. Using an analogy, the hardware binary digits refer to the amount of storage space available (like the number of buckets available to store things), and the information content the filling, which comes in different levels of granularity (fine or coarse, that is, compressed or uncompressed information). When the granularity is finer—when information

3496-409: The c91 decoder was fitted to all subsequent models. New 36xxx models are budget models fitted with low cost digital decoders lacking motor regulation. When Märklin introduced the specially developed C-Sine motor in 2000 these models were numbered 39xxx, some were also produced as 37xxx. Märklin offered many different decoders and kits to upgrade analog locomotives to digital control. A digital decoder

3588-411: The controller, dynamically negotiating an individual address and passing the locomotive description and all available functions to the controller. All control parameters are retained by the decoder in firmware and adjusted using the controller or computer. mfx decoders can also interpret the older Motorola format and so will work with previous central units. Märklin experienced compatibility problems with

3680-451: The decoder, either continuous power (lighting) or momentary (signal, uncoupler, turnout) is provided. K83 decoders are for solenoid (momentary) accessories and K84 for lighting (continuous) accessories, each one controlling up to 4 devices. Automatic braking allows a locomotive to coast relatively gently up to a stop signal at danger. When fed with negative DC the decoder will slow the locomotive smoothly. Track must be sectioned at least once,

3772-400: The definition of inductance the inductance of a solenoid follows as A table of inductance for short solenoids of various diameter to length ratios has been calculated by Dellinger, Whittmore, and Ould. This, and the inductance of more complicated shapes, can be derived from Maxwell's equations . For rigid air-core coils, inductance is a function of coil geometry and number of turns, and

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3864-475: The delay after making a speed change on the controller and the response of the decoder, which allows smooth transitions. All mfx decoders provide motor regulation with 128 speed steps and multiple adjustable parameters, plus 16 switched functions. All are programmable by the Central Station, tools are not required to change parameters. In 2015 Märklin released a new series of retrofit decoders built on

3956-422: The earlier version but Central Station could be set to send either protocol to any decoder so older locomotives could be controlled alongside mfx equipped locomotives. The Central Station incorporated all functionality of the earlier keyboard, memory, and interface modules as well as being able to control up to 8 automatic shuttle (point to point) trains. The hand held Mobile Station 60652 was also offered which has

4048-415: The early 21st century, retail personal or server computers have a word size of 32 or 64 bits. The International System of Units defines a series of decimal prefixes for multiples of standardized units which are commonly also used with the bit and the byte. The prefixes kilo (10 ) through yotta (10 ) increment by multiples of one thousand, and the corresponding units are the kilobit (kbit) through

4140-502: The field is increased by that amount: In most solenoids, the solenoid is not immersed in a higher permeability material, but rather some portion of the space around the solenoid has the higher permeability material and some is just air (which behaves much like free space). In that scenario, the full effect of the high permeability material is not seen, but there will be an effective (or apparent) permeability μ eff such that 1 ≤  μ eff  ≤  μ r . The inclusion of

4232-549: The first Central Station (CS1) leading to a recall and extensive rebuild resulting in CS1 V2. Meantime some important components, especially an mfx compatible booster, were unavailable. Eventually booster 60173 became available for use with any mfx system. ESU, the original developers of CS1, produced V3 software update. This had many of the enhancements offered by CS2, including track layout views for controlling signals and turnouts, and large cab view locomotive control display. From

4324-1577: The first, second, and third kind. Using: B → = ∇ × A → , {\displaystyle {\vec {B}}=\nabla \times {\vec {A}},} The magnetic flux density is obtained as B ρ = μ 0 I 4 π 1 l ρ [ ( R + ρ ) 2 + ζ 2 ( ( m − 2 ) K ( m ) + 2 E ( m ) ) ] ζ − ζ + , {\displaystyle B_{\rho }={\frac {\mu _{0}I}{4\pi }}{\frac {1}{l\,\rho }}\left[{\sqrt {(R+\rho )^{2}+\zeta ^{2}}}{\biggl (}(m-2)K(m)+2E(m){\biggr )}\right]_{\zeta _{-}}^{\zeta _{+}},} B z = μ 0 I 2 π 1 l [ ζ ( R + ρ ) 2 + ζ 2 ( K ( m ) + R − ρ R + ρ Π ( n , m ) ) ] ζ − ζ + . {\displaystyle B_{z}={\frac {\mu _{0}I}{2\pi }}{\frac {1}{l}}\left[{\frac {\zeta }{\sqrt {(R+\rho )^{2}+\zeta ^{2}}}}\left(K(m)+{\frac {R-\rho }{R+\rho }}\Pi (n,m)\right)\right]_{\zeta _{-}}^{\zeta _{+}}.} On

4416-416: The flux density outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can (see Gauss's law for magnetism ). The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form loops. However, the volume outside

4508-473: The full track power available, decoders can use motor feedback and constant adjustment to maintain steady speed regardless of train load or track gradient. Combined with braking and acceleration delay (artificial inertia) these decoders give smooth and exact speeds with reliable slow speed control. A number of different digital systems were developed, but Märklin Digital and DCC (Digital Command Control) are

4600-433: The individual characteristics; gradients and curves require constant adjustment and low speed running is both difficult and liable to stalling. Any train lighting will vary in intensity with the power and be off when the locomotive is stopped. Digital control supplies constant power to the track with the power being switched many times a second to provide the " bits " of data (0 and 1) necessary for control (such digital power

4692-451: The integral. Thus the integral of the up side 1 is equal to the integral of the down side 2. Since we can arbitrarily change the dimensions of the loop and get the same result, the only physical explanation is that the integrands are actually equal, that is, the magnetic field inside the solenoid is radially uniform. Note, though, that nothing prohibits it from varying longitudinally, which in fact, it does. A similar argument can be applied to

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4784-433: The intrinsic inductance and capacitance cannot be done using those for the conventional solenoids, i.e. the tightly wound ones. New calculation methods were proposed for the calculation of intrinsic inductance (codes available at ) and capacitance. (codes available at ) As shown above, the magnetic flux density B {\displaystyle B} within the coil is practically constant and given by where μ 0

4876-409: The level of manipulating bits rather than manipulating data interpreted as an aggregate of bits. In the 1980s, when bitmapped computer displays became popular, some computers provided specialized bit block transfer instructions to set or copy the bits that corresponded to a given rectangular area on the screen. In most computers and programming languages, when a bit within a group of bits, such as

4968-429: The locomotive must return to a fuelling point for replenishment (feedback modules denote the fuelling points). Signals may also be fitted with feedback modules, requiring acknowledgement by the operator as the train passes, just as in real operation. The new controller software provides a cab view of the locomotive to allow control of all parameters. This gives a computer simulation view of the locomotive while controlling

5060-424: The loop a to conclude that the field outside the solenoid is radially uniform or constant. This last result, which holds strictly true only near the center of the solenoid where the field lines are parallel to its length, is important as it shows that the flux density outside is practically zero since the radii of the field outside the solenoid will tend to infinity. An intuitive argument can also be used to show that

5152-782: The magnetic flux density through the centre of the solenoid (in the z direction, parallel to the solenoid's length, where the coil is centered at z =0) can be estimated as the flux density of a single circular conductor loop: Within the category of finite solenoids, there are those that are sparsely wound with a single pitch, those that are sparsely wound with varying pitches (varied-pitch solenoid), and those with varying radii for different loops (non-cylindrical solenoids). They are called irregular solenoids . They have found applications in different areas, such as sparsely wound solenoids for wireless power transfer , varied-pitch solenoids for magnetic resonance imaging (MRI), and non-cylindrical solenoids for other medical devices. The calculation of

5244-410: The main controller (Central Station) or a computer. Märklin locomotives had several motor types and many upgrades were for a particular version. Almost all the first generation decoders had DIP switches to set the address and potentiometers to set motor regulation, requiring tools to open the model and make adjustments. The motor parameters are maximum speed and artificial inertia , in other words

5336-406: The material) and effective permeability (a property of the whole structure) are often confused; they can differ by many orders of magnitude. For an open magnetic structure, the relationship between the effective permeability and relative permeability is given as follows: where k is the demagnetization factor of the core. A finite solenoid is a solenoid with finite length. Continuous means that

5428-469: The name "Märklin Systems" was dropped and once again the system is known as "Märklin Digital". Introduced in 2013, the extended mfx+ digital control system provides additional locomotive parameters and allows feedback with mfx+ equipped locomotives. The virtual fuel state of each mfx+ equipped locomotive can be set and monitored. For steam locomotives, additional parameters such as boiler pressure and fire state can be set, monitored, and controlled. Eventually,

5520-400: The new Central Station. In 2016 Central Station 3 was announced. The main change is a new touch screen which replaces all of the function buttons with on screen options. Only the two speed controllers and emergency stop bar remain as separate controls. Central Station 3+ adds the ability to act as a master unit in a multi controller set up. Decoders are designated mfx and can communicate with

5612-419: The new decoders had 27 speed steps, existing controllers could only send 14 and so the decoders would step up odd steps and down even steps making all 27 steps accessible. The extra functions allowed for other features such as additional lighting and sound. While the small size of speaker that can be fitted into H0 locomotives limits reproduction, built in sound has become a feature of many models. Adjustments to

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5704-556: The new decoders required tools, as before. "Function" was most commonly used for locomotive headlights, F1 & F2 were usually used for other power functions such as smoke units or additional lighting. F3, when available, was commonly used for sound, and F4 usually used to disable artificial inertia for precise control, especially when shunting. These decoders are now designated "fx" to distinguish them from earlier decoders lacking additional switched functions. Function decoders without motor control can also be fitted to carriages providing

5796-408: The orientation of reversible double stranded DNA , etc. Bits can be implemented in several forms. In most modern computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a flip-flop circuit. For devices using positive logic , a digit value of 1 (or a logical value of true) is represented by a more positive voltage relative to

5888-584: The original digital system, but separate function decoders only became available with the enhanced system. A simplified system intended to appeal to beginners and those put off by the then substantial cost of full digital systems, DELTA offered control of up to four locomotives simultaneously. DELTA decoders did not have motor regulation and initially lacked any way of easily changing the address. DELTA has now been discontinued, simplified digital controllers & decoders are offered instead (Mobile Station & 36xxx series locomotives). Early DELTA controllers lacked

5980-443: The physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program . It may be physically implemented with a two-state device. A contiguous group of binary digits is commonly called a bit string , a bit vector, or a single-dimensional (or multi-dimensional) bit array . A group of eight bits is called one  byte , but historically

6072-531: The previously controlled direction. The new 6021 combined control unit & locomotive control with additional function buttons. Miniature switches set the operating mode (old or new protocol) and reduced track voltage for shunting areas. The new Control 80f allowed additional locomotive controllers to be plugged into the right hand side of a 6021, other modules as before. 1997 c91 (60901) decoders provided additional function outputs F1 - F4, 27 speed steps (stop 0 and 1 - 27), and improved motor regulation. Although

6164-576: The problem of loop-back topology (a problem encountered in polarized 2-rail). Conceptually, the entire layout may be controlled from just two wires to the track, but in practice multiple feeds will be required and power to the track is usually separated from power to accessories. The final step to ideal running was the development of motor regulation or speed control (often misleadingly called "load control"). Locomotive motors are controlled using pulse-width modulation which gives much better regulation than conventional analogue control. Additionally, utilizing

6256-517: The representation of 0 . Different logic families require different voltages, and variations are allowed to account for component aging and noise immunity. For example, in transistor–transistor logic (TTL) and compatible circuits, digit values 0 and 1 at the output of a device are represented by no higher than 0.4 V and no lower than 2.6 V, respectively; while TTL inputs are specified to recognize 0.8 V or below as 0 and 2.2 V or above as 1 . Bits are transmitted one at

6348-461: The right hand side of the Central Unit, and up to 16 keyboards could be added to the left hand side, with each keyboard controlling 16 accessories (signals, turnouts, lights, etc.) for a total of 256. For large layouts 6016 Boosters and their own power supplies would provide additional power to layout sections with all Boosters linked to the Central Unit by a ribbon cable. A later accessory was

6440-414: The same way as a single wire, due to the current flowing overall down the length of the solenoid. Applying Ampère's circuital law to the solenoid (see figure on the right) gives us where B {\displaystyle B} is the magnetic flux density , l {\displaystyle l} is the length of the solenoid, μ 0 {\displaystyle \mu _{0}}

6532-424: The size of the byte is not strictly defined. Frequently, half, full, double and quadruple words consist of a number of bytes which is a low power of two. A string of four bits is usually a nibble . In information theory , one bit is the information entropy of a random binary variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known. As

6624-413: The solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer. Of course, if the solenoid is constructed as a wire spiral (as often done in practice), then it emanates an outside field

6716-445: The solenoid is not formed by discrete coils but by a sheet of conductive material. We assume the current is uniformly distributed on the surface of the solenoid, with a surface current density K ; in cylindrical coordinates : K → = I l ϕ ^ . {\displaystyle {\vec {K}}={\frac {I}{l}}{\hat {\phi }}.} The magnetic field can be found using

6808-403: The solenoid is not formed by discrete finite-width coils but by many infinitely thin coils with no space between them; in this abstraction, the solenoid is often viewed as a cylindrical sheet of conductive material. The magnetic field inside an infinitely long solenoid is homogeneous and its strength neither depends on the distance from the axis nor on the solenoid's cross-sectional area. This

6900-471: The solenoid, far away from the ends ( l / 2 − | z | ≫ R {\displaystyle l/2-|z|\gg R} ), this tends towards the constant value B = μ 0 N I / l {\displaystyle B=\mu _{0}NI/l} . For the case in which the radius is much larger than the length of the solenoid ( R ≫ l {\displaystyle R\gg l} ),

6992-414: The stopping area before the signal, and usually also a transition section to prevent short circuits. An electronic control module is switched when the signal changes to danger and changes the track voltage in the stopping area. In 1993 an enhancement to the original system introduced improvements for locomotive control: The changes were entirely compatible with earlier locomotive decoders so any controller

7084-656: The symmetry axis, the radial component vanishes, and the axial field component is B z = μ 0 N I 2 ( z + l / 2 l R 2 + ( z + l / 2 ) 2 − z − l / 2 l R 2 + ( z − l / 2 ) 2 ) . {\displaystyle B_{z}={\frac {\mu _{0}NI}{2}}\left({\frac {z+l/2}{l{\sqrt {R^{2}+(z+l/2)^{2}}}}}-{\frac {z-l/2}{l{\sqrt {R^{2}+(z-l/2)^{2}}}}}\right).} Inside

7176-399: The system producing locomotive decoders and, later, Märklin's first DC command control offering. This first DC offering was later developed into what is now known as Digital Command Control (DCC). The new Märklin Digital system offered simultaneous control of up to 80 locomotives and 256 accessories. 14 locomotive speed steps (stop 0 and 1 - 14) were provided and an accessory "Function" that

7268-577: The thickness of alternating black and white lines. The bit is not defined in the International System of Units (SI). However, the International Electrotechnical Commission issued standard IEC 60027 , which specifies that the symbol for binary digit should be 'bit', and this should be used in all multiples, such as 'kbit', for kilobit. However, the lower-case letter 'b' is widely used as well and

7360-420: The track and individually controlled. Train lighting will always be at full intensity, even when the locomotive is stopped. Signals and turnouts may also be provided with decoders and controlled digitally. The track consists of 2 electrically-grounded rails, and a row of center studs over which the engine's pickup "shoe" glides acquiring the digital-pulsed 16V signal and power. This symmetrical track design solved

7452-613: The two main systems on the market. The systems are electrically compatible and some controllers can simultaneously control both types of decoder. Märklin offered versions of their original digital system for 2-rail users. Märklin first presented the new digital control system at the Nürnberg Toy Fair in 1979. The Motorola based system was officially introduced in 1985, developed by a relatively unknown electronics contractor with most components built by Märklin. In subsequent years, another contractor, Bernd Lenz, would also work on

7544-556: The two possible values of one bit of storage are not equally likely, that bit of storage contains less than one bit of information. If the value is completely predictable, then the reading of that value provides no information at all (zero entropic bits, because no resolution of uncertainty occurs and therefore no information is available). If a computer file that uses n  bits of storage contains only m  <  n  bits of information, then that information can in principle be encoded in about m  bits, at least on

7636-444: The two values of a bit may be represented by two levels of electric charge stored in a capacitor . In certain types of programmable logic arrays and read-only memory , a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In optical discs , a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional bar codes , bits are encoded as

7728-467: Was able to control any locomotive decoder type (a few special function decoders developed earlier were incompatible with the revised protocol, 6021 control units could be set to send old protocol only). Absolute direction control is important for computer controlled layouts so that, after power off, locomotives will restart in the previously controlled direction. Older c90 decoder equipped locomotives will always restart forwards after power off, regardless of

7820-451: Was also used in Morse code (1844) and early digital communications machines such as teletypes and stock ticker machines (1870). Ralph Hartley suggested the use of a logarithmic measure of information in 1928. Claude E. Shannon first used the word "bit" in his seminal 1948 paper " A Mathematical Theory of Communication ". He attributed its origin to John W. Tukey , who had written

7912-460: Was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a paper card or tape . The first electrical devices for discrete logic (such as elevator and traffic light control circuits , telephone switches , and Konrad Zuse's computer) represented bits as the states of electrical relays which could be either "open" or "closed". When relays were replaced by vacuum tubes , starting in

8004-531: Was re-numbered to 60214 a few months later, with more capabilities than 60213. In 2009 a software update for the CS2 was announced which, among other enhancements, adds support for the NMRA DCC protocol. Also in 2009 a new 60653 Mobile Station was announced, completely redesigned with many more features than the earlier model. As before, the new Mobile Station can be used by itself or as an additional controller with

8096-507: Was recommended by the IEEE 1541 Standard (2002) . In contrast, the upper case letter 'B' is the standard and customary symbol for byte. Multiple bits may be expressed and represented in several ways. For convenience of representing commonly reoccurring groups of bits in information technology, several units of information have traditionally been used. The most common is the unit byte , coined by Werner Buchholz in June 1956, which historically

8188-734: Was the basis and many kits also included a permanent magnet and 5 pole armature to upgrade the motor and convert it to DC (such decoders rectify track current to DC for the motor and any accessories, such as lighting or sound). For many years, unlike Digital Command Control , Märklin did not use a plug in connector for the decoder and so conversion involved soldering output wires. Most decoders also provide motor regulation (speed control) with adjustments for acceleration & braking delay (artificial inertia) and maximum speed. DELTA decoders never provided motor regulation and originally had to be set to address 0 for analog operation. mfx decoders provide many additional motor control parameters, all adjusted using

8280-444: Was used for locomotive front and rear headlights or TELEX remote uncoupling. Electronics of the time were relatively expensive and the system used ternary logic to reduce the number of components and cost of devices. Early decoders cost as much as many model locomotives and the expense of upgrading an existing layout was considerable. The original 6020 Central Unit provided track power & generated locomotive commands but required

8372-541: Was used in the punched cards invented by Basile Bouchon and Jean-Baptiste Falcon (1732), developed by Joseph Marie Jacquard (1804), and later adopted by Semyon Korsakov , Charles Babbage , Herman Hollerith , and early computer manufacturers like IBM . A variant of that idea was the perforated paper tape . In all those systems, the medium (card or tape) conceptually carried an array of hole positions; each position could be either punched through or not, thus carrying one bit of information. The encoding of text by bits

8464-405: Was used to represent the group of bits used to encode a single character of text (until UTF-8 multibyte encoding took over) in a computer and for this reason it was used as the basic addressable element in many computer architectures . The trend in hardware design converged on the most common implementation of using eight bits per byte, as it is widely used today. However, because of

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