Fixed-Point NumbersAll computer instructions and data are represented and stored in binary (base 2) form.In therepresentation offixed-pointnumbers, the value of each digit in the number depends on its positionrelative to the fixed decimal point. For example the integer value 53 in base 10 is represented bythe binary or base 2 value 00110101, denoted by5310= 001101012In base 10, this means5310= 5×101+ 3×100Similarly,001101012=0×27+ 0×26+ 1×25+ 1×24+ 0×23+ 1×22+ 0×21+ 1×20=3210+ 1610+ 410+ 110Thus, each bit position represents an increasing power of 2, beginning with 20on the right.Floating-Point NumbersTo represent non-integer numbers, a number representation known asﬂoating-pointmust bedefined. Floating-point numbers are used on computers to approximate a subset of the real numbers.While there are many possible ﬂoating-point number systems, all such systems consist of zero, aset of positive numbers, and the corresponding set of negative numbers.
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