# Johnson Counter

A circuit which is used to count the number of times an event occurs is called a counter. In digital sense, these circuits comprise of bi-stable devices called flip-flops arranged in a particular fashion. Such a chain can be regarded to be a shift register, due to which counters can be considered as an application of shift registers. Either D or JK type flip-flops are preferred while designing the counter circuits. One such counter designed using D flip-flop chain is shown by Figure 1 and is called Johnson counter.

The schematic shows a cascaded arrangement of n flip-flops in which the output of the preceding flip-flop is fed as an input to the immediate next flip-flop. However it is to be noted that the complement output of the last flip-flop Q̅n is back-fed to the first flip-flop in the chain. This arrangement results in a closed loop due to which the bits within the counter continuously circulate within it. Further, the schematic shown in the figure is seen to comprise of n flip-flops due to which it is called n-bit Johnson counter. Further, the counter has preset (P) and clear (C) pins meant to initialize and reset the counter, respectively.

At this instant, it is worthwhile of mentioning that the circuit of Johnson counter differs from that of a ring counter only in one factor. That is, in Johnson counter, complement output of last flip-flop is used as a feed-back while in the ring counter, it is the non-complement one (please put the link of the article on ring counter here), due to which Johnson counter is also called twisted ring counter. This difference causes the Johnson counters to have different sequence of states in comparison with the ring counters. However the mode of data movement remains the same i.e. even here, the bits within the counter shift in their position by one bit position for each clock pulse, similar to that in the case of ring counter.

Table I shows the movement of bits within a 3-bit Johnson counter from its initial state 000. From the table, it is evident that the same data pattern repeats after 6 clock cycles. This means that, in general, n bit Johnson counter has 2n distinct states after which the cycle repeats. As a result, we can consider n bit Johnson counter to be MOD 2n in-nature. The waveforms concerned with the 3-bit Johnson counter are shown by Figure 2.

Now, recall that the ring counter of n-bit length has only n distinct states while the Johnson counter of the same length is seen to have twice its number. Thus we can say that Johnson counters are much better in comparison to ring counters when the question is of state-usage.

### Applications of Johnson Counter

These circuits are extensively used as frequency dividers and pattern recognizers.

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