How to add (all zero state) to the states of linear feedback shift register (LFSR)
What state occurs before you would like the all 0s state? What state would occur after the all 0s?

For instance, in a 5 bit, 00001 becomes 10000, it might be handy to have 00000 between those. 

Normally, the XOR next state logic of a LSFR turns one into the other.

You have to detect 00001 and override the logic to force 00000.

With the normal LSFR logic, the 00000 state would be persistent, so you have to override it one more time to force 10000 after 00000. You could either detect 00000, or remember that you forced one cycle ago, so you have to do the other force this cycle.