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I imagine the difference between DCF77 and a 50Hz clock is similar to the difference between a $40 clock and a $10 clock. :P

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Radio-controlled is pretty much the default around here (and the cheap ones cost perhaps 5 €); I think I've yet to see a grid-powered alarm clock.

Here's an IC used in some alarm clocks that uses the power grid's frequency, along with a list of products that use it: https://www.radiomuseum.org/tubes/tube_lm8560.html

It was mostly used in the common radio alarm clocks, the ones with a 4digit red 7 segment display that were all based on an IC from the 70s that handles everything (minus the radio which is a completely indipendent module).

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