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

Read more about this topic:  Decimal Floating Point, Floating Point Arithmetic Operations

Other articles related to "multiplication":

Church Of The Multiplication
... The Church of the Multiplication of the Loaves and Fishes, shortened to (The Church of the Multiplication), is a Roman Catholic church located in Tabgha, on the northwest shore of ...
Logrithm - History - Predecessors
... The Babylonians sometime in 2000–1600 BC may have invented the quarter square multiplication algorithm to multiply two numbers using only addition, subtraction and a table of squares ... tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of computers ... prosthaphaeresis was used to approximate multiplication and division ...
Classical Hamiltonian Quaternions - Four Operations - Cardinal Operations - Multiplication
... Classical quaternion notation had only one concept of multiplication ... Multiplication of two real numbers, two imaginary numbers or a real number by an imaginary number in the classical notation system was the same operation ... Multiplication of a scalar and a vector was accomplished with the same single multiplication operator multiplication of two vectors of quaternions used this same operation ...
Semifield
... is an algebraic structure with two binary operations, addition and multiplication, which is similar to the field, but with some axioms relaxed ... is a Z-algebra whose nonzero elements form a loop under multiplication ... S with two operations + (addition) and · (multiplication), such that (S,+) is an abelian group, multiplication is distributive on both the left and right, there exists a ...
Multiplication - Exponentiation
... When multiplication is repeated, the resulting operation is known as exponentiation ... For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 23, a two with a superscript three ...