Computer Arithmetic Systems

Computer Arithmetic

Interval Arithmetic, Extended Numbers and Computer Algebra Systems

Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” Historically, this approach resulted in programs that implicitly used certain identities to simplify expressions. These identities, which very likely seemed universally true to the programmers in the heat of writing the CAS, (a...

Computer Arithmetic Conversions between Binary and Decimal Systems

We will first see how to convert a real number in binary form into its decimal equivalent. The key idea is that the binary digits to the left of the binary decimal point increase in factors of 2 for each place moved over. Similarly, the digits to the right of the binary decimal point decrease in factors of 2 for each place moved over. Consider the real number (101.1)2 in binary form. We have (1...

DRAFT: Interval arithmetic, Extended numbers and Computer Algebra Systems (CAS)

Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” We see this kind of goal in programs like Macsyma, Maple, Mathematica. This approach often resulted in programs that implicitly used certain identities to simplify expressions. These identities, which likely seemed universally ...

Modern Computer Arithmetic

A 2009 IEEE Transactions on Computers (TC) guest editorial called computer arithmetic “the mother of all computer research and application topics.” Today, one might question what computer arithmetic still o ers in terms of advancing scienti c research; after all, multiplication and addition haven’t changed. The answer is surprisingly easy: new architectures, processors, problems, application do...