Your explanation here is described in my original reply as "that adding 3 numbers to make two results is much faster in hardware than adding 2 numbers to make one result."
I initially typed a further explanation of "no carry chain is necessary, so each addition becomes constant time", but decided for most readers here, they either wouldn't be hardware experts and wouldn't see why a carry chain was relevant, or would be hardware experts in which case it's already obvious, since full adders are used in loads of things wired like this.
Thankyou for expanding in a lot more detail though.
I initially typed a further explanation of "no carry chain is necessary, so each addition becomes constant time", but decided for most readers here, they either wouldn't be hardware experts and wouldn't see why a carry chain was relevant, or would be hardware experts in which case it's already obvious, since full adders are used in loads of things wired like this.
Thankyou for expanding in a lot more detail though.