  We call `bits' a sequence of devices indexed by positive integers, where
every device can be in two states: $0$ (idle) and $1$ (active). Start from the
`ground state' of the system when all bits are in $0$-state. In our first
Binary Flipping (BF) model, the evolution of the system is the following: at
each time step choose one bit from a given distribution $\mathcal{P}$ on the
integers independently of anything else, then flip the state of this bit to the
opposite. In our second Damaged Bits (DB) model a `damaged' state is added:
each selected idling bit changes to active, but selecting an active bit changes
its state to damaged in which it then stays forever.
  In both models we analyse the recurrence of the system's ground state when no
bits are active. We present sufficient conditions for both BF and DB models to
show recurrent or transient behaviour, depending on the properties of
$\mathcal{P}$. We provide a bound for fractional moments of the return time to
the ground state for the BF model, and prove a Central Limit Theorem for the
number of active bits for both models.
