Mathematica, 8-bit full adder

Remove["Global`*"];
n = 8;
addbit[a_, b_, cin_] := {Xor[a, b, cin], Or[And[a, b], And[cin, Xor[a, b]]]}
num2bool[a_] := If[NumberQ[a], Thread[IntegerDigits[a, 2, n] > 0], Array[a, n]]
truth2int[a_] := FromDigits[Boole@a, 2]
add[a_, b_] := With[{A = num2bool[a], B = num2bool[b]},
   Most@Reverse@
     FoldList[addbit[#2[[1]], #2[[2]], #1[[2]]] &, {False, False},
      Reverse@Transpose[{A, B}]]
   ][[All, 1]]

(* test it works *)
truth2int@add[0, 0] == 0
truth2int@add[1, 0] == 1
truth2int@add[1, 1] == 2
truth2int@add[5, 9] == 14
truth2int@add[2^n - 1, 1] == 0

BooleanMinimize[add[x, y]]