combinational logic
Combinational logic is circuitry with no memory: the output depends only on the inputs right now, never on what happened before. Think of a vending machine's price display that simply shows whatever the current button selection costs — change the buttons and the number changes immediately, and the display holds no recollection of past selections. A combinational circuit is exactly like a mathematical function: feed it the same inputs and you always get the same output, with no hidden state and no past.
Concretely, a combinational circuit is a network of gates with signals flowing strictly forward from inputs to outputs and no feedback loops. Whenever an input changes, the change propagates through the gates and, after a settling time (the propagation delay along the longest path), the outputs reach their final, correct values determined entirely by the present inputs. Because it is purely a function of the inputs, every combinational circuit can be specified by a truth table and built by the sum-of-products recipe. The standard combinational building blocks are the multiplexer (a hardware selector), the decoder and encoder (turning a number into a one-of-many line and back), the adder (and so the arithmetic unit), and the comparator.
Why it matters: combinational logic is half of all digital design. It is where the actual computing happens — adding, selecting, comparing, decoding. The other half is sequential logic, which adds memory and a clock. The crucial honest point is timing: during the brief window after inputs change, while signals are still racing through the gates, a combinational circuit's outputs can momentarily flicker through wrong values (called glitches) before settling. That is harmless inside a clocked system because we only look at the outputs after they have settled — which is precisely the job the clock does.
A 1-bit comparator answering 'is A greater than B?' is combinational: its truth table over (A,B) is (0,0)->0, (0,1)->0, (1,0)->1, (1,1)->0, so the output is A AND (not B), a single gate pair. Present A=1,B=0 and the output is 1 the moment the signals settle; there is nothing to remember.
Same inputs, same output, every time — the defining mark of combinational logic is having no memory.
If a circuit's output ever depends on the order or history of inputs — like a counter that remembers its tally — it is not combinational. The instant feedback or a stored bit enters, you have crossed into sequential logic.