Decimal Floating Point - Floating Point Arithmetic Operations - Multiplication

Multiplication

To multiply, the significands are multiplied while the exponents are added, and the result is rounded and normalized.

e=3; s=4.734612 × e=5; s=5.417242 ----------------------- e=8; s=25.648538980104 (true product) e=8; s=25.64854 (after rounding) e=9; s=2.564854 (after normalization)

Division is done similarly, but that is more complicated.

There are no cancellation or absorption problems with multiplication or division, though small errors may accumulate as operations are performed repeatedly. In practice, the way these operations are carried out in digital logic can be quite complex.

Further information: Booth's multiplication algorithm and Division algorithm