Addition

The combining of two or more quantities using the Plus operator. The individual numbers being combined are called Addends, and the total is called the Sum. The first of several Addends, or ``the one to which the others are added,'' is sometimes called the Augend. The opposite of addition is Subtraction.

While the usual form of adding two $n$-digit Integers (which consists of summing over the columns right to left and ``Carrying'' a 1 to the next column if the sum exceeds 9) requires $n$ operations (plus carries), two $n$-digit Integers can be added in about $2\lg n$ steps by $n$ processors using carry-lookahead addition (McGeoch 1993). Here, $\lg x$ is the Lg function, the Logarithm to the base 2.

See also Addend, Amenable Number, Augend, Carry, Difference, Division, Multiplication, Plus, Subtraction, Sum

References

McGeoch, C. C. ``Parallel Addition.'' Amer. Math. Monthly 100, 867-871, 1993.