Ripple Adders:Time?Complexity
The equations for the sum and carry out for a full adder can be
cout0 = x0•y0 + x0•cin0 + y0•cin0
cout1 = x1•y1 + x1•(x0•y0 + x0•cin0 + y0•cin0) + y1•(x0•y0 + x0•cin0 + y0•cin0)
cout1 = x1•y1 + x1•x0•y0 + x1•x0•cin0 + x1•y0•cin0 + y1•x0•y0 + y1•x0•cin0 + y1•y0•cin0