Who invented the adder, full-adder, half-adder? I didn't find, in the digital design books, who invented the adders.

The same person invented the half-adder and the full-adder?

What's the oldest publication on digital arithmetic design?
In 1966, I was taught by Professor Tom Kilburn at Manchester University.

He said the half adder was sometimes called the Kilburn adder because he invented it!