An encoder converts an active input signal into a binary code representation.
A priority encoder assigns priority to the highest-order input if multiple inputs are active at the same time.

Example: 8-bit Priority Encoder

K-Maps for 4-Bit Priority Encoder

Dout[0]

Simplified Expression:
$D_{\text{out}}[0]=D_{\text{in}}[3]+D_{\text{in}}[2{]}^{\prime }{D}_{\text{in}}[1]$
$\text{Valid}=|D_{\text{in}}$

Dout[1]

Simplified Expression:
$D_{\text{out}}[1]=D_{\text{in}}[2]+D_{\text{in}}[3]$
$\text{Valid}=|D_{\text{in}}$

Verilog Implementation

module PENC4(Din, Dout, Valid);
    input  [3:0] Din;
    output [1:0] Dout;
    output       valid;

    assign Dout[0] = Din[3] | ((!Din[2]) & Din[1]);
    assign Dout[1] = Din[2] | Din[3];
    assign Valid   = |Din;   // reduction OR on Din
endmodule