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| Written by goldeneggs | |||||||||
| Wednesday, 05 November 2008 08:22 | |||||||||
In general, 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. In practice, there are two types of counters:
 Toggle flip-flop. Output is not shown. Red=1, blue=0 In electronics, counters can be implemented quite easily using register-type circuits such as the flip-flop, and a wide variety of designs exist, e.g:
Asynchronous (ripple) counters  Asynchronous Counter created from JK flip-flops. The simplest counter circuit is a single D-type flip flop, 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 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: cycleQ1Q0(Q1:Q0)dec00001011210231134000You 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). Synchronous counters  A 4-bit synchronous counter Where a stable count value is important across several bits, which is the case in most counter systems, synchronous counters are used. These also use flip-flops, either the D-type or the more complex J-K type, but here, each stage is clocked simultaneously by a common clock signal. Logic gates between each stage of the circuit control data flow from stage to stage so that the desired count behaviour is realised. Synchronous counters can be designed to count up or down, or both according to a direction input, and may be presettable via a set of parallel "jam" inputs. Most types of hardware-based counter are of this type. Johnson counters A Johnson counter is a special case of shift register, where the output from the last stage is inverted and fed back as input to the first stage. A pattern of bits equal in length to the shift register thus circulates indefinitely. These counters are sometimes called "walking ring" counters, and find specialist applications, including those similar to the decade counter, digital to analogue conversion, etc. Decade counters Decade counters are a kind of counter that counts in tens rather than having a binary representation. Each output will go high in turn, starting over after ten outputs have occurred. This type of circuit finds applications in multiplexers and demultiplexers, or wherever a scanning type of behaviour is useful. Similar counters with different numbers of outputs are also common. Up-Down Counters It is a combination of up counter and down counter, counting in straight binary sequence. There is an up-down selector. If this value is kept high, counter increments binary value and if the value is low, then counter starts decrementing the count. Template:Sectsub Ring Counters A ring counter is a counter that counts up and when it reaches the last number that is designed to count up to, it will reset itself back to the first number. For example, a ring counter that is designed using 3 JK Flip Flops will count starting from 001 to 010 to 100 and back to 001. It will repeat itself in a 'Ring' shape and thus the name Ring Counter is given. Counters in computer science In 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 finite state machine (FSM), which can perform the following operations on the counter:
The first machine, an FSM plus two counters, is equivalent in power to a Turing machine. transfer
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