Explain the Asynchronous Up-Down Counters?

In some applications a counter must be able to count both down and up and the circuit below is a 3-bit up-down counter. It counts down or up depending on the status of the control signals UP and DOWN When the UP input is at 1 and the DOWN input is at 0 the NAND network between FF0 and FF1 will gate the non-inverted output (Q) of FF0 into the clock input of FF1. Likewise, Q of FF1 will be gated throughout the other NAND network into the clock input of FF2, Therefore the counter will count up.

When the control input UP is at 0 and DOWN is at 1 and the inverted outputs of FF0 and FF1 are gated into the clock inputs of FF1 and FF2 respectively. If the flip-flops are primarily reset to 0's then the counter will go through the following sequence as input pulses are applied.