Governments issue their national currency…. or a governing body does (looking at you EU). So they know exactly how much currency has been created. They also run the official destruction mechanisms for physical currency that’s been in circulation and is now too damaged for use. So they know a good chunk of what is physically destroyed. On top of that they do a rough estimate of how much is unofficially destroyed or lost. Generally, that amount is fairly insignificant compared to the total pool.
As far as digital currency most nations have very strict and robust auditing systems in place to track and validate digital transactions. Digital transactions are difficult to track for humans because there are so many of them. But computers are really good at doing repetitive math and can work out if all the numbers match up pretty easily.
They really don’t need to know an exact number when it comes to currency. Nations aren’t worried about that level of detail. They don’t deal in dollars/euros/yen/etc. They deal in millions/billions/trillions of the currency.
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