Combinationally

Combinationally is an adverb derived from combinational, used to describe actions, processes, or systems that depend on combinations of elements rather than on sequence or memory. In general usage, the term signals that a result follows from current components or inputs through a combination of parts.

In digital electronics, a circuit described as operating combinationally produces outputs that are a function only of the current input values. Such circuits do not contain storage elements and have no memory of past inputs. This distinguishes them from sequential circuits, whose outputs may depend on past inputs and internal state. Typical combinational circuits include adders, multiplexers, decoders, and logic gates arranged to implement a Boolean function.

In combinatorics and related areas, combinationally can be used to describe approaches that construct or count objects by combining parts, without recourse to iterative processes that depend on order or time. In practice, one might study a problem combinationally by deriving a formula based on the number of ways to select or arrange components, then aggregating results across cases. More commonly, the related adverb combinatorially is used in mathematical writing to emphasize counting arguments.

Usage notes: While both forms exist, combinationally is more often encountered in discussions of circuits and hardware design, whereas combinatorially is preferred for counting and enumeration.

See also: Combinational logic, Combinatorics, Sequential logic.