As a kid I heard that circuits like adders were made from boolean algebra AND, OR and NOT gates. I played around on a big paper pad, and finally got a 4 bit ad

As a kid I heard that circuits like adders were made from boolean algebra AND, OR and NOT gates. I played around on a big paper pad, and finally got a 4 bit adder implementation. But since my unit circuit was [A,B]->[S], instead of the canonical [A,B,carry-in]->[S,carry-out], I had to add a second layer of units to propagate the first carry onward. And a third layer of units in case that also generated a carry. Etc. So my circuit had gate of order N^2/2 and depth order of 2*N instead of gate and depth orders of N.