Computer arithmetic systems: algorithms, architecture and implementation
Computer arithmetic systems: algorithms, architecture and implementation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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The representation in which we normally write decimal numbers, for example 276.1069 (1) is nothing more than shorthand symbolic representation for the precise mathematical equivalent 2 × 100 + 7 × 10 + 6 × 1 + 1 × 0.1 + 0 × + 6 × 0.0001 + 9 × 0.0001 (2) or 2 × 102 + 7 × 101 + 6 × 100 + 1 × 10-1 +0 × 10-2 + 6 × 10-3 + 9 × 10-4 (3) Equations (2) and (3) express clearly that the decimal system we use has a base, or radix, R = 10. By analogy, therefore, the binary, or base 2 (i.e. R = 2), system so commonly used with computers can become immediately understandable, as presented below. The notation (1)--often called positional notation because the position of a digit specifies the power of 10 in (3) that is associated with it--effectively hides the real mathematical content of a number.