The bit-sliced index (BSI) was originally defined in [ONQ97]. The current paper introduces the concept of BSI arithmetic. For any two BSI's X and Y on a table T, we show how to efficiently generate new BSI's Z, V, and W, such that Z = X + Y, V = X - Y, and W = MIN(X, Y); this means that if a row r in T has a value x represented in BSI X and a value y in BSI Y, the value for r i n BSI Z will be x + y, the value in V will be x - y and the value i n W will be MIN(x, y). Since a bitmap representing a set of rows is the simplest bit-sliced index, BSI arithmetic is the most straightforward way to determine multisets of rows (with duplicates) resulting from the SQL clauses UNION ALL (addition), EXCEPT ALL (subtraction), and INTERSECT ALL (min) (see [OO00, DB2SQL] for definitions of these clauses). Another contribution of the current paper is to generalize BSI range restrictions from [ONQ97] to a new non-Boolean form: to determine the top k BSI-valued rows, for any meaningful value k between o...