How much more inaccurate is binary integer arithmetic than decimal integer arithmetic? Can the accuracy of binary computers be improved to make them as accurate as decimal computers?
What will be an ideal response?
This is a trick question. In the absence of actual errors (faulty hardware or software), any digital logic system is perfectly accurate; that is, a calculation in one base yields the same result as a calculation in another base. Any so?called inaccuracies result from finite word?lengths (e.g., a 10?bit binary value represents a number to one part in 210 (one in in 1,000) whereas a 10?bit decimal number allows a representation of 1 part in 10,000,000,000). Inaccuracies arise in fractional calculations (remember that a number like ? cannot be represented in a finite number of digits). Similarly, not all decimal fractions can always be represented exactly in binary by a finite number of bits.
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