It is often shown on DMM specifications where resolution is described in digits.  It is common to see 4.5 digits, 5.5 digits, 6.5 digits, and higher.  When reading this, the whole number must be split up from the fraction.

For example, lets look at 4.5 digits, or 4 and 1/2 digits.

The "4" represents full digits, meaning digits that can be represented or shown from 0-9 on the display.

The "1/2", or "0.5" represent the first digit of the reading display and the maximum it can read.  In this case, "1/2" digit means the first digit that can represent the digit 0-1.

Putting it together, 4.5 digits mean the display can show 00000 to 19999.  This is because the first digit can show 0 and 1, and the last "4" proceeding digits can show 0-9.  There is 4 because it is a 4 and a 1/2 digit meter.  This means, if this was to be converted to count, it would be 20000 count, because 4.5 digits mean you can display 00000 to 19999.  The next digit up would change it's range.  Therefore, it would be 20000 count, as this would change it's range.

Another example, lets look at  3.75, or 3 and 3/4 digits.

Typically, 3/4 digit can represent a digit that can read from 0 to 3, and in some cases 0 to 5.  Taking the same idea as the previous example, 3 whole digits mean 3 digits can represent 0-9, and the 3/4 represents the first digit from left.  Putting this together, 3.75 digits can represent display showing 0000 to 3999 before range is changed.  Meaning, an instrument with this digit resolution would have 4000 counts.  

Some manufacturers also use 3/4 to represent digits that can display 0 to 5.  In this case, 3.75 digits can also represent display resolution showing 0000 to 5999.  Converting this to counts, it would be 6000 counts.

Because there are two different use of "3/4", it is important to look at specifications carefully, especially the range of the instrument.  Some manufacturers do not specify counts, so therefore looking at the range would be the best way to determine how much display resolution you can obtain when making measurements.  For example, if the range of the multimeter for DC voltage is 2V, 20V, 200V, 1000V, it can be assumed that most likely the meter has a 1/2 digit.  If it was 5V, 50V, 500V, 1000V, it can be assumed that most likely the meter has a 3/4 digit.