Exercise 3.30. Figure 3.27 shows a ripple-carry adder formed by stringing together n full-adders. This is the simplest form of parallel adder for adding two n-bit binary numbers. The inputs A1, A2, A3, ..., An and B1, B2, B3, ..., Bn are the two binary numbers to be added (each Ak and Bk is a 0 or a 1). The circuit generates S1, S2, S3, ..., Sn, the n bits of the sum, and C, the carry from the addition. Write a procedure ripple-carry-adder that generates this circuit. The procedure should take as arguments three lists of n wires each–the Ak, the Bk, and the Sk–and also another wire C. The major drawback of the ripple-carry adder is the need to wait for the carry signals to propagate. What is the delay needed to obtain the complete output from an n-bit ripple-carry adder, expressed in terms of the delays for and-gates, or-gates, and inverters?

(define (ripple-carry-adder as bs ss c)
  (define (sequence-adder a b s c-out)
    (if (not (null? (cdr a)))
        (let ((new-in (make-wire)))
          (begin
            (full-adder (car a) (car b) new-in (car s) c-out)            
            (sequence-adder (cdr a) (cdr b) (cdr s) new-in)))
        (full-adder (car a) (car b) 0 (car s) c-out)))
  (sequence-adder as bs ss c))