The power will only get through when every bit is off, otherwise it will be blocked by one of the inverted switches. This only happens once every 8 turns. If you'd like it to happen at a different point along the 8 turn cycle you can replace some of the inverted switches with standard voltage switches - any combination will only let power through once during the 8 turn cycle.
If you still don't understand build it and watch the behaviour of the inverted switches and you should get what I mean.
]]>In this case it won't work - firstly clocks don't work like this. The clock will only send a single substep "pulse" every 8 turns and this isn't enough to cause full power. To turn it into full power you need to use something like a bit storage unit, but this will create continuous power from then on. If you want something to be on every 8 turns the easiest way is to connect it in such a way that it will power whenever every bit is in a particular state. This can be done by making the bits power voltage and inverted switches that the power must pass through.
Secondly, as electric floors conduct power the door can never be open when they are on. Pit traps would be more useful (though expensive) here.
For the second question - I'd say the clock is as small as you'll get it to achieve this without thinking up a better binary counter bit design than my one.
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