So for example if you have a very simple oscillator such as: 
How could I control this so that the oscillator is only in operation when a signal (x) is high. And not in operation when it is low?
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5\$\begingroup\$ The answer is obvious but I am not giving it. Study the available type of gates, AND, OR, NAND and NOR. Think of what happens if you replace an inverter with each and select the one that works. \$\endgroup\$– OldfartOct 8, 2018 at 15:32
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I assume you've had enough time to think about this (and I also don't have enough karma to make comments) so I'll give you one possible solution, though it's definitely not the only one. Replace the 3rd inverter with a NAND gate, where one of the inputs is x and the other input is the output from the second inverter. When x is 0, the output is forced to 1 and the whole thing stops oscillating. When x is 1, the output of the NAND gate is the opposite of the output of the second oscillator.
You can see the truth table for a NAND gate here in case you don't get it. http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/nand.html
