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Elegant code for binary append?

I just wrote the add-registers functions to binary add two n-bit registers in Racket (using the add bits function as a helper):

(define (bit-add x y c)
  (values (bitwise-xor x y c) (bitwise-ior (bitwise-and x y)
                                           (bitwise-and x c)
                                           (bitwise-and y c))))

(define (add-registers xs ys)
  (let ([carry 0])
    (values (reverse (for/list ([b1 (reverse xs)] [b2 (reverse ys)])
                       (let-values ([(nb nc) (bit-add b1 b2 carry)])
                         (set! carry nc)
                         nb)))
            carry)))

But I found my code to be pretty ugly. So I wonder if this can be written more succinctly and elegantly?

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The new version add-registers

looks a little nicer here:



(define (add-registers xs ys)
  (for/fold ([carry 0] [bs empty])
     ([b1 (reverse xs)] [b2 (reverse ys)])
     (define-values (nb nc) (bit-add b1 b2 carry))
     (values nc (cons nb bs))))
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