Asynchronous Decade Counters

The binary counters  introduced  in previous post have two to the power n states.  But counters with states less than this number are also possible.  They are designed to have the number of states in their sequences, which are called truncated sequences.  These sequences are achieved by forcing the counter to recycle before going through all of its normal states. A common modulus for counters with truncated sequences is ten.  A counter with ten states in its sequence is called a decade counter.  The circuit below is an implementation of a decade counter.

Once the counter counts to ten (1010), all the flip-flops are being cleared.  Notice that only Q1 and Q3 are used to decode the count of ten.  This is called partial decoding, as none of the other states (zero to nine) have both Q1 and Q3 HIGH at the same time. The sequence of the decade counter is shown in the table below: