For modern electronic computers, mathematical computations are carried out within the arithmetic logic unit (ALU) of its central processing unit (CPU). The numbers stored and manipulated by the computer can be represented in either a fixed-point representation or a floating-point representation. Numbers expressed in fixed-point notation are allotted a fixed number of digits on either side of the decimal point (the "decimal point" is in actuality a binary point for use within the computer because modern computers use the binary number system). A simple example of a fixed-point format is "XX.XX," where the "X" characters represent digits; in this example there are two places represented on each side of the decimal point. A representation of a decimal number in that format is "87.01." However, the number "567.89" could not be represented in the fixed-point format used for this illustration because the "hundreds" component is not allowed (i...