SUMIF, differentiate between 0, 00 and BLANK

In the SUMIF function I need to be able to differentiate between cells with the following content:

• 0, as number or text
• 00, necessarily as text
• 000, also text
• Completely BLANK, as after having pressed DELETE
• BLANK, but with an apostrophe (')

As it is now the SUMIF (and probably also all the other functions, COUNTIF, VLOOKUP, etc.) acts as follows:

• Looking up a 0, 00, 000, etc. counts only cells contaning zeros, both 0, 00, 000, etc., and it does so regardless of the number of zeros
• Looking up a completely BLANK value does the same; i.e. it does not count the really blank cells
• Looking up a BLANK value with apostrophe counts all the blank cells - with or without apostrophe - but not the zeros

Is there a solution to this?

NSV