Combinational Logic
Combinational logic produces outputs that depend only on the present inputs, with no memory of the past.
Definition
A combinational circuit computes its outputs purely from its current inputs. Given the same inputs it always gives the same outputs, with no stored state and no dependence on history. It is a direct hardware realization of a Boolean function.
How it is described
- A truth table lists the output for every input combination.
- A Boolean expression, often in sum-of-products form, states the function algebraically.
- A gate-level schematic shows the actual AND, OR, and NOT structure.
- All three describe the same behavior and can be derived from one another.
Common building blocks
Larger combinational functions are assembled from standard blocks: multiplexers, decoders, encoders, comparators, and adders. Each is itself just a Boolean function realized in gates.
No feedback
A purely combinational circuit has no feedback loop from output back to input. Adding such a loop introduces memory and turns the circuit sequential. Keeping the datapath acyclic is what guarantees a settled, single-valued output.
Timing
Although the logic is memoryless, it is not instantaneous. After inputs change, outputs are valid only once the propagation delay along the longest path has elapsed. During that window outputs may momentarily glitch before settling.
Contrast with sequential logic
Circuits that remember, such as latches, flip-flops, counters, and state machines, are sequential. Most real systems interleave the two: combinational logic computes next values while sequential elements hold state between clock edges.