In the carry-lookahead adders you designed for your previous homework assignment, you used carry propagate (P) and generate (G) signals to form the carry equations.  Design a 4-bit adder that instead uses carry propagate (P) and kill (K) signals.  Recall that K = (A_i + B_i)'.  Write equations for the four carrys (C₄, C₃, C₂, and C₁) in terms of P_i, K_i, and C₀.