In digital logic Digital electronics are systems that represent signals as discrete levels, rather than as a continuous range. In most cases the number of states is two, and these states are represented by two voltage levels: one near to zero volts and one at a higher level depending on the supply voltage in use. These two levels are often represented as "Low& and computing Computing, also known as computer science, is usually defined as the activity of using and improving computer technology, computer hardware and software. It is the computer-specific part of information technology. Computer science is the study and the science of the theoretical foundations of information and computation and their implementation, a counter is a device which stores (and sometimes displays) the number of times a particular event In philosophy, events are objects in time or instantiations of properties in objects. However, a definite definition has not been reached, as multiple theories exist concerning events or process In computing, a process is an instance of a computer program that is being executed. It contains the program code and its current activity. Depending on the operating system , a process may be made up of multiple threads of execution that execute instructions concurrently has occurred, often in relationship to a clock signal In electronics and especially synchronous digital circuits, a clock signal is a particular type of signal that oscillates between a high and a low state and is utilized like a metronome to coordinate actions of circuits. Although the word signal has a number of other meanings, the term is here used for "transmitted energy that can carry. In practice, there are two types of counters:

• Up counters, which increase (increment An increment is an increase of some amount, either fixed or variable. For example one's salary may have a fixed annual increment or one based on a percentage of its current value. A decrease is called a decrement) in value
• Down counters, which decrease (decrement An increment is an increase of some amount, either fixed or variable. For example one's salary may have a fixed annual increment or one based on a percentage of its current value. A decrease is called a decrement) in value

In electronics

In electronics Electronics is the branch of science and technology which makes use of the controlled motion of electrons through different media and vacuum. The ability to control electron flow is usually applied to information handling or device control. Electronics is distinct from electrical science and technology, which deals with the generation,, counters can be implemented quite easily using register-type circuits such as the flip-flop In digital circuits, a flip-flop is a term referring to an electronic circuit that has two stable states and thereby is capable of serving as one bit of memory. Today, the term flip-flop has come to mostly denote non-transparent (clocked or edge-triggered) devices, while the simpler transparent ones are often referred to as latches; however, as, and a wide variety of designs exist, e.g:

• Asynchronous (ripple) counter – changing state bits are used as clocks to subsequent state flip-flops
• Synchronous counter – all state bits change under control of a single clock
• Decade counter – counts through ten states per stage
• Up–down counter – counts both up and down, under command of a control input
• Ring counter – formed by a shift register with feedback connection in a ring
• Johnson counter – a twisted ring counter
• Cascaded counter

Each is useful for different applications. Usually, counter circuits are digital A digital system is a data technology that uses discrete values. By contrast, non-digital (or analog) systems use a continuous range of values to represent information. Although digital representations are discrete, the information represented can be either discrete, such as numbers, letters or icons, or continuous, such as sounds, images, and in nature, and count in natural binary The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers. Many types of counter circuit are available as digital building blocks, for example a number of chips in the 4000 series The 4000 series is a family of industry standard integrated circuits which implement a variety of logic functions using Complementary Metal–Oxide–Semiconductor technology. They were introduced by RCA as CD4000 COS/MOS in 1968, as a lower power and more versatile alternative to the 7400 series of TTL logic chips. Almost all IC manufacturers implement different counters.

Occasionally there are advantages to using a counting sequence other than the natural binary sequence -- such as the binary coded decimal In computing and electronic systems, binary-coded decimal (sometimes called natural binary-coded decimal, NBCD) or, in its most common modern implementation, packed decimal, is an encoding for decimal numbers in which each digit is represented by its own binary sequence. Its main virtue is that it allows easy conversion to decimal digits for counter, a linear feedback shift register A linear feedback shift register is a shift register whose input bit is a linear function of its previous state counter, or a Gray-code The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit counter.

Counters are useful for digital clocks and timers, and in oven timers, VCR clocks, etc.^[1]

Asynchronous (ripple) counter

An asynchronous (ripple) counter is a single D-type flip-flop In digital circuits, a flip-flop is a term referring to an electronic circuit that has two stable states and thereby is capable of serving as one bit of memory. Today, the term flip-flop has come to mostly denote non-transparent (clocked or edge-triggered) devices, while the simpler transparent ones are often referred to as latches; however, as, with its D (data) input fed from its own inverted output. This circuit can store one bit, and hence can count from zero to one before it overflows (starts over from 0). This counter will increment once for every clock cycle and takes two clock cycles to overflow, so every cycle it will alternate between a transition from 0 to 1 and a transition from 1 to 0. Notice that this creates a new clock with a 50% duty cycle In telecommunications and electronics, the duty cycle is the fraction of time that a system is in an "active" state. In particular, it is used in the following contexts: at exactly half the frequency of the input clock. If this output is then used as the clock signal for a similarly arranged D flip-flop (remembering to invert the output to the input), you will get another 1 bit counter that counts half as fast. Putting them together yields a two bit counter:

You can continue to add additional flip-flops, always inverting the output to its own input, and using the output from the previous flip-flop as the clock signal. The result is called a ripple counter, which can count to 2ⁿ-1 where n is the number of bits (flip-flop stages) in the counter. Ripple counters suffer from unstable outputs as the overflows "ripple" from stage to stage, but they do find frequent application as dividers for clock signals, where the instantaneous count is unimportant, but the division ratio In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour overall is. (To clarify this, a 1-bit counter is exactly equivalent to a divide by two circuit; the output frequency is exactly half that of the input when fed with a regular train of clock pulses).

The use of flip-flop outputs as clocks leads to timing skew between the count data bits, making this ripple technique incompatible with normal synchronous circuit In an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. These transitions follow the level change of a special signal called the clock. Ideally, the input to each storage element has reached its final value before the next clock occurs, so the behaviour of the whole circuit can be predicted design styles.

Synchronous counter

A simple way of implementing the logic for each bit of an ascending counter (which is what is depicted in the image to the right) is for each bit to toggle when all of the less significant bits are at a logic high state. For example, bit 1 toggles when bit 0 is logic high; bit 2 toggles when both bit 1 and bit 0 are logic high; bit 3 toggles when bit 2, bit 1 and bit 0 are all high; and so on.

Synchronous counters can also be implemented with hardware finite state machines A finite state machine or finite state automaton (plural: automata), or simply a state machine, is a model of behavior composed of a finite number of states, transitions between those states, and actions. It is similar to a "flow graph" where we can inspect the way in which the logic runs when certain conditions are met. A finite state, which are more complex but allow for smoother, more stable transitions.

Hardware based counters are of this type.

Ring counter

A ring counter is a shift register In digital circuits, a shift register is a cascade of flip flops, sharing the same clock, which has the output of any one but the last flip-flop connected to the "data" input of the next one in the chain, resulting in a circuit that shifts by one position the one-dimensional "bit array" stored in it, shifting in the data (a cascade connection of flip-flops) with the output of the last one connected to the input of the first, that is, in a ring. Typically a pattern consisting of a single 1 bit is circulated, so the state repeats every N clock cycles if N flip-flops are used. It can be used as a cycle counter of N states.

Johnson counter

A Johnson counter (or switchtail ring counter, twisted-ring counter, walking-ring counter, or Moebius counter) is a modified ring counter, where the output from the last stage is inverted and fed back as input to the first stage.^[2][3][4] A pattern of bits equal in length to twice the length of the shift register thus circulates indefinitely. These counters find specialist applications, including those similar to the decade counter, digital to analog conversion, etc.

Decade counter

A decade counter is one that counts in decimal digits, rather than binary. A decimal counter may have each digit binary encoded (that is, it may count in binary-coded decimal In computing and electronic systems, binary-coded decimal (sometimes called natural binary-coded decimal, NBCD) or, in its most common modern implementation, packed decimal, is an encoding for decimal numbers in which each digit is represented by its own binary sequence. Its main virtue is that it allows easy conversion to decimal digits for, as the 7490 The following is a list of 7400 series digital logic integrated circuits. The SN7400 series originated with TTL integrated circuits made by Texas Instruments. Because of the popularity of these parts, they were second-sourced by other manufacturers who kept the 7400 sequence number as an aid to identification of compatible parts. As well, integrated circuit did) or other binary encodings (such as the bi-quinary encoding of the 7490 The following is a list of 7400 series digital logic integrated circuits. The SN7400 series originated with TTL integrated circuits made by Texas Instruments. Because of the popularity of these parts, they were second-sourced by other manufacturers who kept the 7400 sequence number as an aid to identification of compatible parts. As well, integrated circuit). Alternatively, it may have a "fully decoded" or one-hot output code in which each output goes high in turn; the 4017 The 4000 series is a family of industry standard integrated circuits which implement a variety of logic functions using Complementary Metal–Oxide–Semiconductor technology. They were introduced by RCA as CD4000 COS/MOS in 1968, as a lower power and more versatile alternative to the 7400 series of TTL logic chips. Almost all IC manufacturers was such a circuit. The latter type of circuit finds applications in multiplexers In electronics, a multiplexer or mux is a device that performs multiplexing; it selects one of many analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2n inputs has n select lines, which are used to select which input line to send to the output and demultiplexers, or wherever a scanning type of behavior is useful. Similar counters with different numbers of outputs are also common.

The decade counter is also known as a mod-counter.

Up–down counter

A counter that can change state in either direction, under control an up–down selector input, is known as an up–down counter. When the selector is in the up state, the counter increments its value; when the selector is in the down state, the counter decrements the count.

In computer science

In computability theory Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive, a counter is considered a type of memory. A counter stores a single natural number In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition; or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century (initially zero Zero, written 0, is both a number and the numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, oh,) and can be arbitrarily many digits long. A counter is usually considered in conjunction with a finite-state machine A finite state machine or finite state automaton (plural: automata), or simply a state machine, is a model of behavior composed of a finite number of states, transitions between those states, and actions. It is similar to a "flow graph" where we can inspect the way in which the logic runs when certain conditions are met. A finite state (FSM), which can perform the following operations on the counter:

• Check whether the counter is zero
• Increment the counter by one
• Decrement the counter by one (if it's already zero, this leaves it unchanged).

The following machines are listed in order of power, with each one being strictly more powerful than the one below it:

1. Deterministic or non-deterministic FSM plus two counters
2. Non-deterministic FSM plus one stack In computer science, a stack is a last in, first out abstract data type and data structure. A stack can have any abstract data type as an element, but is characterized by only two fundamental operations: push and pop. The push operation adds to the top of the list, hiding any items already on the stack, or initializing the stack if it is empty
3. Non-deterministic FSM plus one counter
4. Deterministic FSM plus one counter
5. Deterministic or non-deterministic FSM

For the first and last, it doesn't matter whether the FSM is a deterministic finite-state machine or a nondeterministic finite-state machine In the theory of computation, a nondeterministic finite state machine or nondeterministic finite automaton is a finite state machine where for each pair of state and input symbol there may be several possible next states. This distinguishes it from the deterministic finite automaton (DFA), where the next possible state is uniquely determined. They have equivalent power. The first two and the last one are levels of the Chomsky hierarchy Within the field of computer science, specifically in the area of formal languages, the Chomsky hierarchy is a containment hierarchy of classes of formal grammars.

The first machine, an FSM plus two counters, is equivalent in power to a Turing machine A Turing machine is a theoretical device that manipulates symbols contained on a strip of tape. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "Turing" machine was described by Alan Turing in 193. See the article on register machines for a proof.

Mechanical counters

Long before electronics became common, mechanical devices were used to count events. These typically consist of a series of disks mounted on an axle, with the digits 0 through 9 marked on their edge. The right most disk moves one increment with each event. Each disk except the left-most has a protrusion that, after the completion of one revolution, moves the next disk to the left one increment. Such counters were originally used to control manufacturing processes, but were later used as odometers An odometer indicates distance traveled by a car or other vehicle. The device may be electronic, mechanical, or a combination of the two. The word derives from the Greek words hodós, meaning "path" or gateway and "métron", "measure" for bicycles and cars and in fuel dispensers A fuel dispenser is a machine at a filling station that is used to pump gasoline, diesel, CNG, CGH2, HCNG, LPG, LH2, ethanol fuel, biofuels like biodiesel, kerosene, or other types of fuel into vehicles. Fuel dispensers are also known as bowsers ., petrol pumps (in Commonwealth countries), or gas pumps (in North America). One of the largest manufacturers was the Veeder-Root company, and their name was often used for this type of counter.^[5]

References

1. ^ http://www.play-hookey.com/digital/synchronous_counter.html
2. ^ Arun Kumar Singh. Digital Principles Foundation of Circuit Design and Application. New Age Publishers. ISBN The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H. Smith and others in 1966 8122417590. http://books.google.com/books?id=13Wi37h2A-oC&pg=PA113&dq=switchtail+ring+counter+johnson&as_brr=3&ei=umTxSPXeKZH2sQP6muHZBg&sig=ACfU3U29vJPSflqg7sngLSbt5OxDp6fMvQ.
3. ^ Paul Horowitz and Winfield Hill (1989). The Art of Electronics. Cambridge University Press. ISBN The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H. Smith and others in 1966 0521370957. http://books.google.com/books?id=bkOMDgwFA28C&pg=PA667&dq=ring+counter+walking&as_brr=3&ei=NGbxSLrfIIuoswP_oqmdBw&sig=ACfU3U0nWT1AwZt_wgUnAedWxa8X6iDktw.
4. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics. Newnes. ISBN The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H. Smith and others in 1966 0750698667. http://books.google.com/books?id=uah1PkxWeKYC&pg=PA401&dq=moebius+ring+counter+johnson&as_brr=3&ei=z2bxSO3hN4XWsgOa243rBg&sig=ACfU3U38T_bIIfEQqOjEIxVzFKp8_oyd6w.
5. ^ http://www.veeder.com/page/vr_history

It is used to count the rank of the athletes in the games.[common wealth,olumpics]

See also

• Time to digital converter

Categories: Numeration Numeration or numeral systems are about the names and naming systems that are used in the spoken/written language for numbers, and the digit symbols and notational system used to write numbers with digits | Digital circuits

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