Wiring Up a Function
A combinational circuit has outputs depending only on current inputs—it has no memory. (Circuits with memory are sequential).
Designing follows a strict recipe:
- Specify: Build a truth table listing outputs for every input combo.
- Derive: Read 1-rows to form a sum-of-products formula.
- Draw: Map terms to gates (AND, OR, NOT).
| Circuit Type | Behavior | Output Logic |
|---|---|---|
| Odd Detector | Outputs 1 when 2-bit input is odd | Passes low bit directly |
| Majority Circuit | Outputs 1 when inputs are 1 | Sum of AND-pairs |
Any truth table maps mechanically to hardware.
Real-World Limits
Practical design involves strict physical constraints:
- Fan-in: Max inputs a single gate accepts (wide functions use gate trees).
- Fan-out: Max gate inputs one output can safely drive.
- Gate Count & Depth: Fewer gates reduce cost; fewer gates in series (shallow depth) reduce propagation delay.
| Feature | Combinational | Sequential |
|---|---|---|
| Memory | None (pure function of present inputs) | Yes (latches and flip-flops) |
Common Pitfall: Expecting a combinational circuit to remember past states. The same inputs always yield the exact same outputs.