A new design of a low-power reversible Vedic multiplier

In recent years, there has been an increasing tendency towards designing circuits based on reversible logic, and has received much attention because of preventing internal power dissipation. In digital computing systems, multiplier circuits are one of the most fundamental and practical circuits used in the development of a wide range of hardware such as arithmetic circuits and Arithmetic Logic Unit (ALU). Vedic multiplier, which is based on Urdhva Tiryakbhayam (UT) algorithm, has many applications in circuit designing because of its high speed in performing multiplication compared to other multipliers. In Vedic multipliers, partial products are obtained through vertical and cross multiplication. In this paper, we propose four 2 x 2 reversible Vedic multiplier blocks and use each one of them in its right place. Then, we propose a 4 x 4 reversible Vedic multiplier using the four aforementioned multipliers. We prove that our design leads to better results in terms of quantum cost, number of constant inputs and number of garbage outputs, compared to the previous ones. We also expand our proposed design to n x n multipliers which enable us to develop our proposed design in every dimension. Moreover, we propose a formula in order to calculate the quantum cost of our proposed n x n reversible Vedic multiplier, which allows us to calculate the quantum cost even before designing the multiplier.