Either circuit is capable of
adding two binary digits together. The mathematical "rules"
of how to add bits together are intrinsic to the hard-wired
logic of the circuits. If we wanted to perform a different
arithmetic operation with binary bits, such as
multiplication, we would have to construct another circuit.
The above circuit designs will only perform one function:
add two binary bits together. To make them do something else
would take re-wiring, and perhaps different componentry.
In this sense, digital
arithmetic circuits aren't much different from analog
arithmetic (operational amplifier) circuits: they do exactly
what they're wired to do, no more and no less. We are not,
however, restricted to designing digital computer circuits
in this manner. It is possible to embed the mathematical
"rules" for any arithmetic operation in the form of digital
data rather than in hard-wired connections between gates.
The result is unparalleled flexibility in operation, giving
rise to a whole new kind of digital device: the