Tying inputs means wiring two or more inputs of a gate to the same signal, so they always carry the same value. With both inputs of a 2-input gate tied to A:
- AND or OR: output A. The gate just passes A through, since = A and = A.
- NAND or NOR: output . The gate becomes an inverter.
- XOR: output always 0, because the inputs can never differ.
- XNOR: output always 1, because the inputs always match.
The NAND and NOR cases are why a universal gate can supply its own inverters.
A related trick is holding one input at a constant:
- NAND with one input at 1 inverts the other. NAND with a 0 is stuck at 1.
- NOR with one input at 0 inverts the other. NOR with a 1 is stuck at 0.
- XOR with a 1 inverts; XOR with a 0 passes through. See xor identities.
In real circuits, unused inputs must never be left floating, since an unconnected CMOS input can drift and make the gate misbehave. Tie an unused input to a used one, or to the constant that doesn't affect the result: 1 for AND and NAND, 0 for OR and NOR.