Question

Q2 (50 pts): Please prove that the carry-out signal, ck, from bit position k-1 of a ripple-carry adder can be expressed as ck = Xk@yk田Sk, where Xk and yk are the two inputs and sk s the sum bit, at the bit position k. Hint: consider the fact sk = Xk@ykBck when simplifying expression xk@yk田Sk.

Answer 1

Full adder circuit is shown below here, x_k,y_k are inputs s_k is sum bit c_k + 1 = (x_ky_k) + (X_k + y_k) c_k = x_ky_k + (x_ky_k + x_k y_k) c_k = x_ky_k + x_ky_k c_k + x_k y_kc_k c_k + 1 = x_k + y_k + c_k hence, c_k + 1 is called carry out signal