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14_pdfsam_2 - Fixed-Point Numbers All computer instructions...

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Fixed-Point Numbers All computer instructions and data are represented and stored in binary (base 2) form. In the representation of fixed-point numbers, the value of each digit in the number depends on its position relative to the fixed decimal point. For example the integer value 53 in base 10 is represented by the binary or base 2 value 00110101, denoted by 53 10 = 00110101 2 In base 10, this means 53 10 = 5 × 10 1 + 3 × 10 0 Similarly, 00110101 2 = 0 × 2 7 + 0 × 2 6 + 1 × 2 5 + 1 × 2 4 + 0 × 2 3 + 1 × 2 2 + 0 × 2 1 + 1 × 2 0 = 32 10 + 16 10 + 4 10 + 1 10 Thus, each bit position represents an increasing power of 2, beginning with 2 0 on the right. Floating-Point Numbers To represent non-integer numbers, a number representation known as floating-point must be defined. 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, a set of positive numbers, and the corresponding set of negative numbers.
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