Modern computers use unsigned integer arithmetic, fixed point arithmetic, two’s complement arithmetic, and floating point arithmetic.
a. By examining a binary number, can you tell which number system it represents?
b. Why are there so many ways of representing numeric values?
c. Do we need them all?
What will be an ideal response?
a. No. Remember that binary numbers have no intrinsic meaning and you cannot determine the meaning of a given number. However, you can guess the meaning of a string of binary values because the string may ‘make sense’ when interpreted in a particular way. For example, if you see a string of bits and notice that when interpreted as ASCII characters the string says ‘Hello world”, it is very likely to be ASCII text and not a floating?point number that looks like this string.
b. People invent things and then make improvements. Moreover, different representations have different properties; for example, two’s complement representation makes the operation of addition and subtraction identical although this complicates division and multiplication.
c. A single binary format could be devised to deal with all number types – but that would complicate the logic circuits that are used to implement the system.
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