, where n is the vector length, and the
result is always positive (in the range 
). For
example,
Arithmetic operators applied to vectors treat the vectors as unsigned binary numbers. If the vectors are of unequal length, the shorter vector is prepended with a vector of zeros to make the lengths equal. Thus
[0,1,1,0] + [1,0]is equivalent to
[0,1,1,0] + [0,0,1,0]
The arithmetic operator is then applied to the unsigned binary numbers
represented by the two vectors, yielding an unsigned binary
representation of the result, of the same length as the argument
vectors. The operators are the same as they are on integers, except
the result is modulo , where n is the vector length, and the
result is always positive (in the range ). For
example,
[0,1,1,0]
+ [0,0,1,0]
= [1,0,0,0]
and
[1,1,1,0]
+ [0,0,1,0]
= [0,0,0,0]
[N.B. Since the arithmetic is modular, it doesn't actually matter whether we look at it as signed or unsigned, except that extension is always by zeros. It would make sense to introduce a special kind of vector that sign-extends rather than zero-extending, to allow signed arithmetic. Or at least a sign-extension operator.]