In the following truth table, V = 1 if and only if the input is valid. D0 D1…

Concept

An encoder maps an active input line to a binary code. A priority encoder handles the case where several input lines are active at once: it fixes a priority order and outputs the code of the highest-priority active line. A separate Valid (V) output signals whether any input line is active at all. The don't-care (x) entries on the lower-priority inputs are the signature: once a higher-priority input is 1, the lower inputs no longer affect the output.

Applying it to this table

Read the output code as X0X1 with X0 as the most-significant bit, matching the table's column values:

1. All inputs 0 → V = 0: nothing is active, so the output is marked invalid.

2. D0 = 1 (lowest priority) → X0X1 = 00, V = 1.

3. D1 = 1 → X0X1 = 01, with D0 shown as x (D0 is ignored once D1 is active).

4. D2 = 1 → X0X1 = 10, with D0, D1 = x.

5. D3 = 1 (highest priority) → X0X1 = 11, with all lower inputs = x.

So the 2-bit output always names the highest-priority active line (Dᵢ → i) and V flags validity — exactly a 4-to-2 priority encoder with a valid output.

Cross-check by elimination

• Plain encoder: has no don't-cares and gives a wrong code when two inputs are high simultaneously — the table's x entries rule this out.

• Decoder: does the reverse mapping (a code in, exactly one line out); here the data lines are inputs and the code is the output.

• Multiplexer / Demultiplexer: both require separate select lines, which this table has none of, and a (de)mux moves a single value rather than producing a priority code.