In all cases, however, the task that the algorithm is to accomplish must be definable. That is, the definition may involve mathematical or logic terms or a compilation of data or written instructions, but the task itself must be one that can be stated in some way. In terms of ordinary computer usage, this means that algorithms must be programmable, even if the tasks themselves turn out to have no solution. In computational devices with a built_in microcomputer logic, this logic is a form of algorithm. As computers increase in complexity, more and more software_program algorithms are taking the form of what is called hard software.

In mathematics, method of solving a problem by repeatedly using a simpler computational method. A basic example is the process of long division in arithmetic. The term algorithm is now applied to many kinds of problem solving that employ a mechanical sequence of steps, as in setting up a computer program. The sequence may be displayed in the form of a flowchart in order to make it easier to follow. As with algorithms used in arithmetic, algorithms for computers can range from simple to highly complex.

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