An encoder is a combinational circuit that converts 2^n input lines, where only one line is active at any time, into n output lines. It performs the reverse operation of a decoder by encoding multiple inputs into fewer outputs. A specific example is the 4x2 encoder with four inputs (A0 to A3) and two outputs (Y1 and Y0). The truth table shows how each activated input corresponds to unique binary output values: for instance, if A1 alone is active among others inactive, it produces an output of "01"; similarly for other cases like when only A3 or another single input activates. Logical expressions derived from this are Y0 = A1 + A3 and Y1 = A2 + A3.