https://youtu.be/QGlWCQXBDHQ
Imagine that we look at some examples of addition of two binary numbers
through small window (that includes three neighbor bit triples for two
numbers and their sum). Two neighbor windows should be consistent, and
we can draw a graph that shows the consistency requirements. Then this
graph can be simplified using some natural rules, and finally we get a
simple algorithm for binary addition (zig-zag: right -- left -- right
passes)