Show the truth table for a 4-2 priority encoder where the LSB has the highest priority, as shown below. Note that you are allowed to use input (and output) don’t care conditions to reduce the number of rows in your truth table.
The correct answer and explanation is:
Truth Table for a 4-to-2 Priority Encoder (LSB has highest priority)
In a 4-to-2 priority encoder, there are 4 input lines and 2 output lines. The inputs are typically labeled I3, I2, I1, I0, where I0 is the least significant bit (LSB) and has the highest priority in this configuration. Only one output represents the position of the highest-priority active input.
Here is the truth table using don’t care conditions (X) to simplify where lower-priority inputs do not affect the output:
| I3 | I2 | I1 | I0 | Y1 | Y0 |
|---|---|---|---|---|---|
| X | X | X | 1 | 0 | 0 |
| X | X | 1 | 0 | 0 | 1 |
| X | 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 0 | – | – |
Explanation (300 Words)
A priority encoder assigns a binary value to the highest-priority active input. In this 4-to-2 encoder, there are four inputs (I3, I2, I1, I0) and two binary outputs (Y1, Y0). Usually, higher input numbers (I3 being most significant) have the highest priority, but in this design, the least significant input (I0) has the highest priority.
That means if I0 is high (1), it takes precedence over all other inputs, regardless of their state. The encoder ignores higher-numbered inputs if a lower-priority input is active. If I0 = 1, then the output is 00. If I0 = 0 and I1 = 1, then I1 takes priority, and the output becomes 01. Similarly, if both I0 and I1 are 0 but I2 = 1, the output is 10. If only I3 = 1, then it gets priority, giving an output of 11.
When all inputs are zero (0000), the output is undefined or may include an additional valid signal like a valid or enable output to indicate whether the output is valid.
To reduce the truth table size, don’t care conditions (X) are used for inputs with lower priority once a higher-priority input is active. This simplification avoids listing all 16 possible input combinations, instead focusing only on scenarios where the highest-priority 1 appears.
This logic helps reduce hardware complexity in digital systems by ensuring that only the most important signal is encoded at any time.