combinational logic
A form of digital circuit logic where the current outputs are entirely a function of the current inputs, without having a memory of previous inputs or states.
combinational logic: circuits with no memory, only math
Combinational logic is a class of digital circuits in which output values depend solely on the current input values. There is no feedback, no storage, no state. Whatever logical result the circuit produces, it produces instantly (within propagation delay) based on what is fed in right now. A simple AND gate is combinational logic: you apply two input signals, and the output follows the truth table with no regard for what happened a microsecond earlier.
The circuit is built from basic logic gates: AND, OR, NOT, NAND, NOR, XOR. These gates are combined so their outputs feed into further gates, but crucially, no output ever loops back to feed an earlier stage in a way that creates feedback. The resulting network is a directed acyclic graph, mathematically speaking. Boolean algebra governs the whole behavior. A multiplexer, a decoder, an adder, a comparator: all are combinational logic circuits.
Where combinational logic sits
Combinational logic forms the stateless half of digital design. The other half is sequential logic, which uses registers, flip-flops, and clocks to store state and create memory. Real systems mix both: a microprocessor uses combinational logic to compute results, but sequential logic to hold data and coordinate timing across clock cycles. A simple shift register is mostly flip-flops (sequential), while its control decoder is mostly gates (combinational).
Propagation delay is the main constraint. A signal entering a combinational circuit must travel through several logic levels before the output settles. A typical small-scale IC gate has a delay of a few nanoseconds per level; larger circuits with many levels can add up. Designers must budget for this when chaining combinational stages together, or inserting combinational logic between clock-synchronized stages in a pipeline.
The term "combinational" reflects the fact that the output is a logical combination of the inputs. There is no other word for it in common use within the trade, though one occasionally hears "acyclic logic" or "purely combinatorial." It is opposed to "sequential logic," which is the standard pairing you will encounter in any digital design text or data sheet.