4060 counter hardware question
Some parts guarantee that every time power is applied after having been absent for any duration, they will start up in a known state.  Many other parts have no such guarantee.  Internal elements in those parts will tend to remain in their present state if current is neither pushed into nor pulled out of them.  There is usually some parasitic internal leakage whose exact characteristics are unpredictable beyond the fact that it is small.  To deal with this, the device will use supplied power to supply as much current as is needed (usually a very small amount) to ensure that any element which is supposed to be high, remains so.  As long as such elements remain high, other elements that need to remain low will be able to draw out any current that leaks into them.

If you remove power from the 4060, it will no longer be able to keep "topping off" any circuit elements that are supposed to remain high and it is likely that, after awhile, enough current would leak out of such elements to make them go low.  Depending upon the exact manufacturing characteristics of the part, however, it might take seconds or even hours for that to occur [if the part was manufactured from perfect materials that had absolutely no contaminants, it might take days or even years].

Note that this chip has an active-high reset.  That means that during the process of removing and re-applying power, there is nothing that would force the part to an all-zeroes state.  If the part had an active-low reset which was normally tied to VDD, then when VDD goes to ground the level on that pin would be below the level of any internal circuit nodes that might be holding "1"s, thus possibly triggering a reset [though depending upon the design of the reset circuitry, the voltage on the reset pin might need to be below VDD to trigger a reset].  With an active-high reset that simply sits at ground potential, however, there is nothing to trigger a reset and thus the part is likely to just retain its state (at least for awhile).

Note, btw, that while one can't particularly expect something like a 4060 to always reset when power is cycled, one also can't particularly expect that it will never reset as a result of power-cycling.  Even if 999 chips from a batch of 1,000 happen to be capable of holding their state for an hour without power, there's no guarantee that the last one would do likewise, since a chip would be considered "fully functional" even if it couldn't hold its state for a second without power.