Although the nuclear power plant is a common example of a hard real-time application, there's a better one close at hand: audio.
You have a stream of 8- (phone), 16- (CD), or 24- (pro recording) bit samples moving through the system at anywhere from 6k to 100k per second. Drop one and you might not notice it, but the hardware cleverly batches them up into blocks. If you're not done with one block before the next one comes in, you will notice it.
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