values is just as valid as unscaling the values, adding the real values, and then scaling the result, and the former is much easier and faster. In either approach, though, the two added numbers must be scaled the same. For other operations, the scaling is very important. Multiplication, for instance, needs to take into account that both numbers are scaled. As an example, consider two real world values A and B. The real world multiplication of these real world values is: A * B = P If they are instead represented with a scale factor of Z, and these scaled representations are subsequently multiplied, the result is the following: AZ * BZ = Q AZ is the scaled real world value of A, or simply the product of A * Z, and likewise, BZ is the scaled representation of B. After the scaled multiplication, the answer is not written PZ, because the value stored in PZ is not the answer. This can be seen by rearranging the statement, where each line in the following is equivalent: AZ * BZ = Q A * Z * B * Z = Q (A * B) * Z * Z = Q P * Z * Z = Q PZ * Z = Q In line 4, P substitutes A * B. It follows that the result of AZ * BZ (which is Q) is not PZ, but rather PZ * Z. If PZ were the answer, it could be stored directly since it has the scale factor built in, as is the case with addition and subtraction. For multiplication, however, the product of two scaled values has an extra scaling built in. As long as this is taken into account, there is still no need to convert AZ and BZ into A and B before performing the operation; the result must be divided by Z before storing it back. After this, PZ will be stored as the result of the multiplication, which is indeed the scaled representation of the result of A * B (the desired answer) rather than the result of AZ * BZ (which is still scaled). Common scaling scenarios Fractional values scaled to integers As previously described, many older processors (and possibly some current ones) do not natively support fractional mathematics. In this case, fractional values can be scaled into integers by multiplying them by ten to the power