# Counter (digital)

Last updated Voltage changes on the 5 outputs of the binary counter counting from 00000, left to 11111 (or 31), right (vertically).

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. The most common type is a sequential digital logic circuit with an input line called the clock and multiple output lines. The values on the output lines represent a number in the binary or BCD number system. Each pulse applied to the clock input increments or decrements the number in the counter.

## Contents

A counter circuit is usually constructed of a number of flip-flops connected in cascade. Counters are a very widely used component in digital circuits, and are manufactured as separate integrated circuits and also incorporated as parts of larger integrated circuits.

## Electronic counters

In electronics, counters can be implemented quite easily using register-type circuits such as the flip-flop, and a wide variety of classified into:

• 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
• Modulus 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 and 4500 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 Gray-code counter.

Counters are useful for digital clocks and timers, and in oven timers, VCR clocks, etc. 

### Asynchronous (ripple) counter

An asynchronous (ripple) counter is a single d-type flip-flop, 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 flip-flop (remembering to invert the output to the input), one will get another 1 bit counter that counts half as fast. Putting them together yields a two-bit counter:

CycleQ1Q0(Q1:Q0)dec
0000
1011
2102
3113
4000

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 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 design styles.

### Synchronous counter

In synchronous counters, the clock inputs of all the flip-flops are connected together and are triggered by the input pulses. Thus, all the flip-flops change state simultaneously (in parallel). The circuit below is a 4-bit synchronous counter. The J and K inputs of FF0 are connected to HIGH. FF1 has its J and K inputs connected to the output of FF0, and the J and K inputs of FF2 are connected to the output of an AND gate that is fed by the outputs of FF0 and FF1. A simple way of implementing the logic for each bit of an ascending counter (which is what is depicted in the adjacent image) 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.

A decade counter is one that counts in decimal digits, rather than binary. A decade counter may have each (that is, it may count in binary-coded decimal, as the 7490 integrated circuit did) or other binary encodings. "A decade counter is a binary counter that is designed to count to 1010 (decimal 10). An ordinary four-stage counter can be easily modified to a decade counter by adding a NAND gate as in the schematic to the right. Notice that FF2 and FF4 provide the inputs to the NAND gate. The NAND gate outputs are connected to the CLR input of each of the FFs."  A decade counter is one that counts in decimal digits, rather than binary. It counts from 0 to 9 and then resets to zero. The counter output can be set to zero by pulsing the reset line low. The count then increments on each clock pulse until it reaches 1001 (decimal 9). When it increments to 1010 (decimal 10) both inputs of the NAND gate go high. The result is that the NAND output goes low, and resets the counter to zero. D going low can be a CARRY OUT signal, indicating that there has been a count of ten.

### Ring counter

A ring counter is a circular shift register which is initiated such that only one of its flip-flops is the state one while others are in their zero states.

A ring counter is a shift register (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 bit is circulated so the state repeats every n clock cycles if n flip-flops are used.

### Johnson counter

A Johnson counter (or switch-tail ring counter, twisted ring counter, walking ring counter, or Möbius counter) is a modified ring counter, where the output from the last stage is inverted and fed back as input to the first stage.    The register cycles through a sequence of bit-patterns, 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, digital-to-analog conversion, etc. They can be implemented easily using D- or JK-type flip-flops.

## Computer science counters

In computability theory, a counter is considered a type of memory. A counter stores a single natural number (initially zero) and can be arbitrarily long. A counter is usually considered in conjunction with a finite-state 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:

1. Deterministic or non-deterministic FSM plus two counters
2. Non-deterministic FSM plus one stack
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 automaton or a nondeterministic finite automaton. They have the same 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.

### Web counter

A web counter or hit counter is a computer software program that indicates the number of visitors, or hits, a particular webpage has received. Once set up, these counters will be incremented by one every time the web page is accessed in a web browser.

The number is usually displayed as an inline digital image or in plain text or on a physical counter such as a mechanical counter. Images may be presented in a variety of fonts, or styles; the classic example is the wheels of an odometer.

Web counter was popular in the mid to late 1990s and early 2000s, later replaced by more detailed and complete web traffic measures.

### Computer based counters

Many automation systems use PC and laptops to monitor different parameters of machines and production data. Counters may count parameters such as the number of pieces produced, the production batch number, and measurements of the amounts of material used.

## Mechanical counters

Long before electronics became common, mechanical devices were used to count events. These are known as tally counters. They typically consist of a series of disks mounted on an axle, with the digits zero through nine 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 used as odometers for bicycles and cars and in tape recorders, fuel dispensers, in production machinery as well as in other machinery. One of the largest manufacturers was the Veeder-Root company, and their name was often used for this type of counter. 

Hand held tally counters are used mainly for stocktaking and for counting people attending events.

Electromechanical counters were used to accumulate totals in tabulating machines that pioneered the data processing industry.

## Related Research Articles

A logic gate is an idealized or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device. Digital electronics, digital technology or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is much easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

In digital circuits, a shift register is a cascade of flip flops, sharing the same clock, in which the output of each flip-flop is connected to the "data" input of the next flip-flop in the chain, resulting in a circuit that shifts by one position the "bit array" stored in it, "shifting in" the data present at its input and 'shifting out' the last bit in the array, at each transition of the clock input.

In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state.

Verilog, standardized as IEEE 1364, is a hardware description language (HDL) used to model electronic systems. It is most commonly used in the design and verification of digital circuits at the register-transfer level of abstraction. It is also used in the verification of analog circuits and mixed-signal circuits, as well as in the design of genetic circuits. In 2009, the Verilog standard was merged into the SystemVerilog standard, creating IEEE Standard 1800-2009. Since then, Verilog is officially part of the SystemVerilog language. The current version is IEEE standard 1800-2017.

In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present value of its input signals but on the sequence of past inputs, the input history as well. This is in contrast to combinational logic, whose output is a function of only the present input. That is, sequential logic has state (memory) while combinational logic does not. The 4000 series is a CMOS logic family of integrated circuits (ICs) first introduced in 1968 by RCA. Almost all IC manufacturers active during this initial era fabricated models for this series. It is still in use today. An adder is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units or ALU. They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations.

In electronic instrumentation and signal processing, a time to digital converter is a device for recognizing events and providing a digital representation of the time they occurred. For example, a TDC might output the time of arrival for each incoming pulse. Some applications wish to measure the time interval between two events rather than some notion of an absolute time.

A synchronous circuit is a digital circuit in which the changes in the state of memory elements are synchronized by a clock signal. In a sequential digital logic circuit, data is stored in memory devices called flip-flops or latches. The output of a flip-flop is constant until a pulse is applied to its "clock" input, upon which the input of the flip-flop is latched into its output. In a synchronous logic circuit, an electronic oscillator called the clock generates a string of pulses, the "clock signal". This clock signal is applied to every storage element, so in an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. 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 exactly. Practically, some delay is required for each logical operation, resulting in a maximum speed at which each synchronous system can run.

Clock skew is a phenomenon in synchronous digital circuit systems in which the same sourced clock signal arrives at different components at different times. The instantaneous difference between the readings of any two clocks is called their skew.

In digital circuits and machine learning, one-hot is a group of bits among which the legal combinations of values are only those with a single high (1) bit and all the others low (0). A similar implementation in which all bits are '1' except one '0' is sometimes called one-cold. In statistics, dummy variables represent a similar technique for representing categorical data. Metastability in electronics is the ability of a digital electronics system to persist for an unbounded time in an unstable equilibrium or metastable state. In digital logic circuits, a digital signal is required to be within certain voltage or current limits to represent a '0' or '1' logic level for correct circuit operation; if the signal is within a forbidden intermediate range it may cause faulty behavior in logic gates the signal is applied to. In metastable states, the circuit may be unable to settle into a stable '0' or '1' logic level within the time required for proper circuit operation. As a result, the circuit can act in unpredictable ways, and may lead to a system failure, sometimes referred to as a "glitch". Metastability is an instance of the Buridan's ass paradox.

A ring counter is a type of counter composed of flip-flops connected into a shift register, with the output of the last flip-flop fed to the input of the first, making a "circular" or "ring" structure. XOR gate is a digital logic gate that gives a true output when the number of true inputs is odd. An XOR gate implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both".

A frequency divider, also called a clock divider or scaler or prescaler, is a circuit that takes an input signal of a frequency, , and generates an output signal of a frequency:

The serial binary adder or bit-serial adder is a digital circuit that performs binary addition bit by bit. The serial full adder has three single-bit inputs for the numbers to be added and the carry in. There are two single-bit outputs for the sum and carry out. The carry-in signal is the previously calculated carry-out signal. The addition is performed by adding each bit, lowest to highest, one per clock cycle. In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems. An incremental encoder is a linear or rotary electromechanical device that has two output signals, A and B, which issue pulses when the device is moved. Together, the A and B signals indicate both the occurrence of and direction of movement. Many incremental encoders have an additional output signal, typically designated index or Z, which indicates the encoder is located at a particular reference position. Also, some encoders provide a status output that indicates internal fault conditions such as a bearing failure or sensor malfunction.

State encoding assigns a unique pattern of ones and zeros to each defined state of a finite-state machine (FSM). Traditionally, design criteria for FSM synthesis were speed, area or both. Following Moore's law, with technology advancement, density and speed of integrated circuits have increased exponentially. With this, power dissipation per area has inevitably increased, which has forced designers for portable computing devices and high-speed processors to consider power dissipation as a critical parameter during design consideration.

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