By displaying only 10 of the thirteen digits, the calculator seems to the user as a “black field” that computes exponentials, cosines, etc. to 10 digits of accuracy. For the calculator to compute features like exp, log and cos to within 10 digits with affordable effectivity, it wants a few extra digits to work with. It just isn’t exhausting to find a easy rational expression that approximates log with an error of 500 models within the final place. Thus computing with thirteen digits provides an answer correct to 10 digits. By maintaining these further three digits hidden, the calculator presents a easy model to the operator.
The IEEE binary standard doesn’t use either of these strategies to represent the exponent, however as an alternative makes use of a biased illustration. In the case of single precision, where the exponent is stored in eight bits, the bias is 127 (for double … Read More