As a first example of useful combinational logic, let’s build a device that
can add two binary digits together. We can quickly calculate what the answers
should be:

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 102 

So we well need two inputs (a and b) and two outputs. The low order output
will be called Σ because it represents the sum, and the high order output
will be called Cout because it represents the carry

The truth table is

Simplifying boolean equations or making some Karnaugh map will produce the
same circuit shown below, but start by looking at the results. The Σ
column is our familiar XOR gate, while the Cout column is
the AND gate. This device is called a half-adder for reasons that will make
sense in the next section.

or in ladder logic

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