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Digital. Works or doesn't. If the power supply is too weak, the current will be too high, the voltage will drop off and the device will not work. The fuse may or may not save the power supply, depending how high the current gets.
I have lived with several Zen masters - all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.
That's why I wrote "Supposedly", just because there is a standard doesn't mean people are following it.
And to complicate things further there are more than one standard, the original EIAJ standard actually specifies the outer barrel as positive and the inner pin negative, while the later IEC standard doesn't specify polarity as far as I know.