By contrast, a normalized floating point number always has a non-zero digit after the decimal point. This permits the most accuracy in the mantissa, since all five digit places are used for the fraction and help to encode the most information. Most computers store the results of arithmetic computations in normalized form.

However, it takes time to normalize a number. For example,

     0.30000 x 108     multiplied by    0.20000 x 106

gives an answer of 0.06000×10¹⁴, which is not normalized. Logic circuitry notices this and shifts the mantissa to the left while subtracting 1 from the exponent to get the normalized answer: 0.60000×10¹³. But this takes more time. Some hardware has separate instructions that allow you to choose to normalize after the arithmetic has occurred, or to not normalize at all.