Computer Number Systems

As the arithmetic applications grow rapidly, it is important for computer engineers to be well informed of the essentials of computer number systems and arithmetic processes.

With the remarkable progress in the very large scale integration (VLSI) circuit technology, many complex circuits unthinkable yesterday become components easily realizable today. Algorithms that seemed impossible to implement now have attractive implementation possibilities for the future. This means that not only the conventional computer arithmetic methods, but also the unconventional ones are worth investigation in new designs.

Numbers play an important role in computer systems. Numbers are the basis and object of computer operations. The main task of computers is computing, which deals with numbers all the time.

Humans have been familiar with numbers for thousands of years, whereas representing numbers in computer systems is a new issue. A computer can provide only finite digits for a number representation (fixed word length), though a real number may be composed of infinite digits.

Because of the tradeoffs between word length and hardware size, and between propagation delay and accuracy, various types of number representation have been proposed and adopted. In this book, we introduce the Conventional Radix Number System and Signed-Digit Number System, both belonging to the Fixed-Point Number System, as well as the Floating-Point Number System. Two additional number systems, the ...

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