 Counter

This article is about the term counter used in electronics and computing. For other uses, see Counter (disambiguation).
In digital logic and computing, a counter is a device which stores (and sometimes displays) the number of times a particular event or process has occurred, often in relationship to a clock signal.
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Electronic counters
In electronics, counters can be implemented quite easily using registertype circuits such as the flipflop, and a wide variety of classifications exist:
 Asynchronous (ripple) counter – changing state bits are used as clocks to subsequent state flipflops
 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 in nature, and count in natural binary. Many types of counter circuits are available as digital building blocks, for example a number of chips in the 4000 series implement different counters.
Occasionally there are advantages to using a counting sequence other than the natural binary sequence—such as the binary coded decimal counter, a linear feedback shift register counter, or a Graycode 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 JKtype flipflop, with its J (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 at exactly half the frequency of the input clock. If this output is then used as the clock signal for a similarly arranged D flipflop (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 twobit counter:
Cycle Q1 Q0 (Q1:Q0)dec 0 0 0 0 1 0 1 1 2 1 0 2 3 1 1 3 4 0 0 0 You can continue to add additional flipflops, always inverting the output to its own input, and using the output from the previous flipflop as the clock signal. The result is called a ripple counter, which can count to 2^{n} − 1 where n is the number of bits (flipflop 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 overall is (to clarify this, a 1bit 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 flipflop outputs as clocks leads to timing skew between the count data bits, making this ripple technique incompatible with normal synchronous circuit 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, which are more complex but allow for smoother, more stable transitions.
Hardwarebased counters are of this type.
Decade counter
A decade counter is one that counts in decimal digits, rather than binary. A decade counter may have each digit binary encoded (that is, it may count in binarycoded decimal, as the 7490 integrated circuit did) or other binary encodings (such as the biquinary encoding of the 7490 integrated circuit). Alternatively, it may have a "fully decoded" or onehot output code in which each output goes high in turn (the 4017 is such a circuit). The latter type of circuit finds applications in multiplexers 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 modcounter when it counts to ten (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). A Mod Counter that counts to 64 stops at 63 because 0 counts as a valid digit.
Up/down counter
A counter that can change state in either direction, under the control of 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.
Ring counter
Main article: Ring counterA ring counter is a Shift Register (a cascade connection of flipflops) 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 bit is circulated so the state repeats every n clock cycles if n flipflops are used.It can be used as a cycle counter of n states.
Johnson counter
Main article: Ring counterA Johnson counter (or switchtail ring counter, twistedring counter, walkingring 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]} The register cycles through a sequence of bitpatterns, whose length is equal to twice the length of the shift register, continuing indefinitely. These counters find specialist applications, including those similar to the decade counter, digitaltoanalog conversion, etc. They can be implemented easily using D or JKtype flipflops.
Computer science counters
Main article: Register machineIn computability theory, a counter is considered a type of memory. A counter stores a single natural number (initially zero) and can be arbitrarily many digits long. A counter is usually considered in conjunction with a finitestate machine (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:
 Deterministic or nondeterministic FSM plus two counters
 Nondeterministic FSM plus one stack
 Nondeterministic FSM plus one counter
 Deterministic FSM plus one counter
 Deterministic or nondeterministic FSM
For the first and last, it doesn't matter whether the FSM is a deterministic finitestate machine or a nondeterministic finitestate machine. They have equivalent power. The first two and the last one are levels of the Chomsky hierarchy.
The first machine, an FSM plus two counters, is equivalent in power to a Turing machine. See the article on counter 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 leftmost 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 for bicycles and cars and in fuel dispensers. One of the largest manufacturers was the VeederRoot company, and their name was often used for this type of counter.^{[5]}
References
 ^ http://www.playhookey.com/digital/synchronous_counter.html
 ^ Arun Kumar Singh. Digital Principles Foundation of Circuit Design and Application. New Age Publishers. ISBN 8122417590. http://books.google.com/books?id=13Wi37h2AoC&pg=PA113&dq=switchtail+ring+counter+johnson.
 ^ Paul Horowitz and Winfield Hill (1989). The Art of Electronics. Cambridge University Press. ISBN 0521370957. http://books.google.com/books?id=bkOMDgwFA28C&pg=PA667&dq=ring+counter+walking.
 ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics. Newnes. ISBN 0750698667. http://books.google.com/books?id=uah1PkxWeKYC&pg=PA401&dq=moebius+ring+counter+johnson.
 ^ http://www.veeder.com/page/vr_history
See also
Categories: Numeration
 Digital circuits
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