The so-called sum-of-powers-of-two arithmetic has the advantage of using simple shift and thus avoiding multiplications operations. In this work, we provide a feasible RLS adaptive filter algorithm employing the SOPOT representation. This reduces the computational burden of the RLS algorithm. Therefore, leading to a reduction in the power consumption from a hardware implementation point of view, which is an important feature in the developing of smaller, lighter and more power-efficient portable devices.