⁵In the early days of personal computers, many microprocessor chips lacked floating-point processing capability. As a result, floating-point calculations had to be implemented in software, with programmed algorithms instructing the microprocessor how to do floating-point arithmetic. Later, floating-point processor chips were added alongside the regular microprocessor to implement these algorithms in hardware rather than emulated them through software, resulting in increased processing speed. After that, these floating-point circuits were simply added to the internal architecture of microprocessor chips as a standard feature. Even now, however, computer programmers understand that floating-point math requires more processor cycles than integer math, and should be avoided in applications where speed is essential and floating-point representation is not. In applications demanding a small microprocessor chip and optimum speed (e.g. embedded systems), fixed-point notation is best for representing numbers containing fractional quantities.