Counter
Encyclopedia
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
.
, counters can be implemented quite easily using register-type circuits such as the flip-flop
, and a wide variety of classifications exist:
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 Gray-code counter.
Counters are useful for digital clocks and timers, and in oven timers, VCR clocks, etc.
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
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 counters can also be implemented with hardware finite state machine
s, which are more complex but allow for smoother, more stable transitions.
Hardware-based counters are of this type.
, as the 7490 integrated circuit did) or other binary encodings (such as the bi-quinary encoding
of the 7490 integrated circuit). Alternatively, it may have a "fully decoded" or one-hot output code in which each output goes high in turn (the 4017 is such a circuit). The latter type of circuit finds applications in multiplexer
s 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 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.
(a cascade connection of flip-flop
s) 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.It can be used as a cycle counter of n states.
They can be implemented easily using D- or JK-type flip-flops.
, 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 finite-state machine (FSM), which can perform the following operations on the counter:
The following machines are listed in order of power, with each one being strictly more powerful than the one below it:
For the first and last, it doesn't matter whether the FSM is a deterministic finite-state machine or a nondeterministic finite-state 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 machine
s for a proof.
s for bicycles and cars and in fuel dispenser
s. One of the largest manufacturers was the Veeder-Root company, and their name was often used for this type of counter.
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...
, a counter is a device which stores (and sometimes displays) the number of times a particular event
Event (philosophy)
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.-Kim’s Property-Exemplification Account of Events:...
or process
Process (computing)
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.A computer program is a...
has occurred, often in relationship to a clock signal
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...
.
Electronic counters
In electronicsElectronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
, counters can be implemented quite easily using register-type circuits such as the flip-flop
Flip-flop (electronics)
In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information. 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...
, and a wide variety of classifications exist:
- 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
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
in nature, and count in natural binary
Binary numeral system
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...
. Many types of counter circuits are available as digital building blocks, for example a number of chips in the 4000 series
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, and are still in use today. They were introduced by RCA as CD4000 COS/MOS series in 1968, as a lower power and more versatile...
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 JK-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 cycleDuty cycle
In engineering, the duty cycle of a machine or system is the time that it spends in an active state as a fraction of the total time under consideration....
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:
| 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 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
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
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
Synchronous circuit
A synchronous circuit is a digital circuit in which the parts are synchronized by a clock signal.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...
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 machine
Finite state machine
A finite-state machine or finite-state automaton , or simply a state machine, is a mathematical model used to design computer programs and digital logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states...
s, which are more complex but allow for smoother, more stable transitions.
Hardware-based 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 binary-coded decimalBinary-coded decimal
In computing and electronic systems, binary-coded decimal is a digital encoding method for numbers using decimal notation, with each decimal digit represented by its own binary sequence. In BCD, a numeral is usually represented by four bits which, in general, represent the decimal range 0 through 9...
, as the 7490 integrated circuit did) or other binary encodings (such as the bi-quinary encoding
Bi-quinary coded decimal
Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including the Colossus. The term bi-quinary indicates that the code comprises both a two-state and a five-state component...
of the 7490 integrated circuit). Alternatively, it may have a "fully decoded" or one-hot output code in which each output goes high in turn (the 4017 is such a circuit). The latter type of circuit finds applications in multiplexer
Multiplexer
In electronics, a multiplexer is a device that selects one of several 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...
s 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 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
A ring counter is a Shift RegisterShift 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...
(a cascade connection of flip-flop
Flip-flop
Flip-flops, thongs, Japanese sandals, or jandals are an open type of outdoor footwear, consisting of a flat sole held loosely on the foot by a Y-shaped strap, like a thin thong, that passes between the first and second toes and around either side of the foot...
s) 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.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. 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 theoryComputability 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...
, a counter is considered a type of memory. A counter stores a single natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
(initially zero
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills 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...
) and can be arbitrarily many digits 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:
- Deterministic or non-deterministic FSM plus two counters
- Non-deterministic FSM plus one stackStack (data structure)In computer science, a stack is a last in, first out abstract data type and linear data structure. A stack can have any abstract data type as an element, but is characterized by only three fundamental operations: push, pop and stack top. The push operation adds a new item to the top of the stack,...
- Non-deterministic FSM plus one counter
- Deterministic FSM plus one counter
- 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. They have equivalent power. The first two and the last one are levels of the Chomsky hierarchy
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
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. 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...
. See the article on counter machine
Counter machine
A counter machine is an abstract machine used in formal logic and theoretical computer science to model computation. It is the most primitive of the four types of register machines...
s 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 odometerOdometer
An odometer or odograph is an instrument that indicates distance traveled by a vehicle, such as a bicycle or automobile. The device may be electronic, mechanical, or a combination of the two. The word derives from the Greek words hodós and métron...
s for bicycles and cars and in fuel dispenser
Fuel dispenser
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...
s. One of the largest manufacturers was the Veeder-Root company, and their name was often used for this type of counter.