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Counters

 

Counters are an important group of sequential logic systems. A counter may be any circuit, which, within certain limits, has a defined relationship between the number of input pulses and the state of the output variables. As each output variable can have only two values, for n outputs, there are 2" possible output combinations, although often only some of these are used. It is

 
 

Fig. 2.40 - State table of a Fig. 2.41 - Output states of a straight binary

straight binary counter. up-counter as a function of time.

 

 

unimportant which number is assigned to which combination, but it is useful to choose a representation which can subsequently be easily processed. The simplest circuits are obtained for the straight binary notation.

Figure 2.40 shows the relationship between the number, Z, of input pulses and the values of output variables z,-, for a 4-bit straight binary counter. If this table is read from top to bottom, two patterns emerge:

1) an output variable zt always changes state when the next lower value Zj -1 changes from 1 to 0.

2) an output variable z; always changes state when all lower variables z,-_!,..., z0 have the value 1 and a new pulse arrives.

These patterns can also be seen in the timing diagram in Fig. 2.41. Pattern (1) is the basis of an asynchronous counter (ripple gounter), whereas pattern (2) yields the synchronous counter.

Occasionally, counters are required, whose output state is reduced by 1 for each count pulse. The operational principle of such a down-counter can also be inferred from the table in Fig. 2.40 by reading it from the bottom up. It follows that

la) an output variable z; of a down-counter changes state whenever the next lower variable z,--! changes from 0 to 1.

2a) an output variable z, of a down-counter always changes state when all

lower variables zt _,,..., z0 have the value 0 and a new clock pulse

arrives.


Date: 2015-01-12; view: 898


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