An encoder is a circuit that changes a set of signals into a code. Let’s
begin making a 2-to-1 line encoder truth table by reversing the 1-to-2 decoder
truth table.

This truth table is a little short. A complete truth table would be

One question we need to answer is what to do with those other inputs? Do
we ignore them? Do we have them generate an additional error output? In many
circuits this problem is solved by adding sequential logic in order to know not
just what input is active but also which order the inputs became active.

A more useful application of combinational encoder design is a binary to
7-segment encoder. The seven segments are given according

Our truth table is:

Deciding what to do with the remaining six entries of the truth table is
easier with this circuit. This circuit should not be expected to encode an
undefined combination of inputs, so we can leave them as “don’t care” when we
design the circuit. The equations were simplified with karnaugh maps.

The collection of equations is summarised here:

The circuit is:

And the corresponding ladder diagram:

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