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The "count" of a multimeter refers to how large a number it can display before it has to change measurement ranges, and how many digits it shows total. This affects how precise a measurement the meter can display (note: this doesn't necessarily reflect absolute accuracy, just precision of the numbers it can report.)

First, the total number of digits of the count matches the digit count of the display.

A x00 count multimeter only displays 3 digits, while a x000 shows 4 digits. So a 200 count meter could read 19.9 volts, while a 2000 could read 19.91 for the same input.

Second, the value of the first digit indicates when the meter needs to "move up" to the next range. A 2000 count multimeter would read 19.99 volts as 19.99, but at 20 would have to read 020.0, loosing a digit of precision. The same thing happens at higher and lower ranges, each time having to move when the top digit reaches 2.

For comparison, a 4000 count multimeter would up-range whenever the top digit gets to 4, allowing it to read 20-39.99 volts with two decimal places where the 2000 cannot.

I suspect, but cannot confirm, the count limits in digital meters are due to the A/D converter used, and the number of output bits it has. This matches up with the common count values being close to powers of two.

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