ALU Design: 1-bit Arithmetic Unit
This full adder circuit was actually invented by Konrad Zuse for his Z3 computer. The Z3 was also built out of relays just like the computer I'm building however he completed his first ... by quite some way ... back in 1941 ... in wartime Berlin. I think it's fair to say that Zuse's machine could be considered the first functional computer (as all previous 'computers' were mechanical calculators) and the efficiency of this design is quite impressive — using the 'dual rail' carry lines to cut down on the switch count and to keep everything within two relays. There's a simulation of this circuit if you'd like to see an interactive version of this circuit rather than staring at a dry old diagram.
As always, this 4PDT design is fine for those with 4PDT relays ... I'm using the smaller DPDT ones so I'll need to double up the relay count. I therefore transform the above diagram to the following: