binary-string-adder.clj

(def add
  {[\0 \0 \0] \0
   [\0 \0 \1] \1
   [\0 \1 \0] \1
   [\0 \1 \1] \0
   [\1 \0 \0] \1
   [\1 \0 \1] \0
   [\1 \1 \0] \0
   [\1 \1 \1] \1})

(def carry
  {[\0 \0 \0] \0
   [\0 \0 \1] \0
   [\0 \1 \0] \0
   [\0 \1 \1] \1
   [\1 \0 \0] \0
   [\1 \0 \1] \1
   [\1 \1 \0] \1
   [\1 \1 \1] \1})

(defn fill [s n]
  (take n (concat s (repeat \0))))

(defn add-bits [{:keys [sum c]} [a b]]
  {:sum (cons (add [a b c]) sum)
   :c (carry [a b c])})

(defn sum->str [{:keys [sum c]}]
  (apply str c sum))

(defn add-binary-strings [x y]
  (let [n  (max (count x) (count y))
        xs (fill (reverse x) n)
        ys (fill (reverse y) n)]
    (->> (map vector xs ys)
         (reduce add-bits {:sum nil, :c \0})
         sum->str)))