A 2-bit encoder taking four input lines (a, b, c, d) has the following encoding scheme with respect to each activated incoming line: a only ->01, b only ->11, c only ->00, d only ->10, a & d ->01, b & c->11. All other incoming activations are "don't care" cases.

1- Build a truth table for this encoder.

2- What are the POS expressions for this encoder?

3- Draw the circuit using only inverters, AND, and OR gates.