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'Simple Counting Machine' printed from http://nrich.maths.org/

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In this problem a circuit has been set up. There are two switches on the left, two logic gates in the middle and two bulbs on the right.

Currently the gates are both set to XOR. They can be changed to any of the following: AND, NAND, OR, NOR, XNOR. Any switch or gate can be altered by clicking on the blue square in its top left hand corner. If you are unsure about the meaning of the logic gates, take a look at Circuit Maker

Can you set the gates so that the number of bulbs which are on is the same as the number of switches which are on? In other words:
when both switches are off both bulbs are off,
when either switch is on one bulb is on,
when both switches are on both bulbs are on.

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Other circuits to try to construct

Can you set the gates so that:

when both switches are on both bulbs are on,
the rest of the time - both bulbs are off;

when both switches are off both bulbs are on,
the rest of the time - both bulbs are off;

when both switches are off both bulbs are off,
when one switch is on both bulbs are on,
when both switches are on one bulb is on.

Experiment further with the effects of the different settings to create similar problems: choose a setting for the two gates, describe clearly the effect of your circuit and challenge a partner to figure out your settings.

If you liked this problem you may like to build your own circuit boards with interesting properties using the Circuit Maker interactivity, or try the harder Adding Machine problem.