Draw the truth table of a 4-to-2 priority encoder.
The correct answer and explanation is:
Truth Table for a 4-to-2 Priority Encoder
(Assuming active-high inputs D3 to D0, with D3 having the highest priority and D0 the lowest)
| D3 | D2 | D1 | D0 | Y1 | Y0 |
|---|---|---|---|---|---|
| 1 | X | X | X | 1 | 1 |
| 0 | 1 | X | X | 1 | 0 |
| 0 | 0 | 1 | X | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | X | X |
Explanation (300 words)
A 4-to-2 priority encoder is a digital circuit that encodes four input signals into two output bits based on a priority system. The four input lines are labeled D3, D2, D1, and D0, with D3 having the highest priority and D0 the lowest. The two outputs Y1 and Y0 represent a binary number that identifies the highest-priority input line that is active (set to 1).
The main function of a priority encoder is to reduce multiple inputs into a binary code representing the position of the highest-priority active input. Unlike a standard encoder, it also resolves conflicts when more than one input is active simultaneously by giving preference to the input with the highest priority.
Let us analyze the truth table:
- When D3 is 1, it overrides all other inputs regardless of their states. The output is 11 (binary for 3).
- If D3 is 0 and D2 is 1, then D2 takes control, and the output becomes 10 (binary for 2).
- If both D3 and D2 are 0 but D1 is 1, the output is 01 (binary for 1).
- If only D0 is 1, then the output is 00 (binary for 0), showing the lowest-priority input.
- If none of the inputs are active (all 0), the outputs are marked as don’t-care conditions (X), since no valid signal is present.
This logic allows digital systems to prioritize tasks or data inputs, which is essential in applications like interrupt controllers, communication systems, and data multiplexing. The simplicity and efficiency of the encoder reduce the complexity of digital circuits by focusing only on the most significant active signal.