As kmcamara discovered, this is exactly the kind of problem that VLOOKUP is intended to solve, and using vlookup is arguably the simplest of the alternative ways to get the job done.
In addition to the three parameters for lookup_value, table_range to be searched, and the column_index for return values, VLOOKUP takes an optional fourth argument that the Excel documentation calls the "range_lookup".
Expanding on deathApril's explanation, if this argument is set to TRUE (or 1) or omitted, the table range must be sorted in ascending order of the values in the first column of the range for the function to return what would typically be understood to be the "correct" value. Under this default behavior, the function will return a value based upon an exact match, if one is found, or an approximate match if an exact match is not found.
If the match is approximate, the value that is returned by the function will be based on the next largest value that is less than the lookup_value. For example, if "12AT8003" were missing from the table in Sheet 1, the lookup formulas for that value in Sheet 2 would return '2', since "12AT8002" is the largest value in the lookup column of the table range that is less than "12AT8003". (VLOOKUP's default behavior makes perfect sense if, for example, the goal is to look up rates in a tax table.)
However, if the fourth argument is set to FALSE (or 0), VLOOKUP returns a looked-up value only if there is an exact match, and an error value of #N/A if there is not. It is now the usual practice to wrap an exact VLOOKUP in an IFERROR function in order to catch the no-match gracefully. Prior to the introduction of IFERROR, no matches were checked with an IF function using the VLOOKUP formula once to check whether there was a match, and once to return the actual match value.
Though initially harder to master, deusxmach1na's proposed solution is a variation on a powerful set of alternatives to VLOOKUP that can be used to return values for a column or list to the left of the lookup column, expanded to handle cases where an exact match on more than one criterion is needed, or modified to incorporate OR as well as AND match conditions among multiple criteria.
Repeating kcamara's chosen solution, the VLOOKUP formula for this problem would be:
=VLOOKUP(A1,Sheet1!A$1:B$600,2,FALSE)