Improved algorithms for non-restoring division and square root

This dissertation focuses on improving the non-restoring division and square root algorithm. Although the non-restoring division algorithm is the fastest and has less complexity among other radix-2 digit recurrence division algorithms, there are some possibilities to enhance its performance. To improve its performance, two new approaches are proposed here. In addition, the research scope is extended to seek an efficient algorithm for implementing non-restoring square root, which has similar steps to non-restoring division. For the first proposed approach, the non-restoring divider with a modified algorithm is presented. The new algorithm changes the order of the flowchart, which reduces one unit delay of the multiplexer per every iteration. In addition, a new method to find a correct quotient is presented and it removes an error that the quotient is always odd number after a digit conversion from a digit converter from the quotient with digits 1 and -1 to conventional binary number. The second proposed approach is a novel method to find a quotient bit for every iteration, which hides the total delay of the multiplexer with dual path calculation. The proposed method uses a Most Significant Carry (MSC) generator, which determines the sign of each remainder faster than the conventional carry lookahead adder and it eventually reduces the total delay by almost 22% compared to the conventional non-restoring division algorithm. Finally, an improved algorithm for non-restoring square root is proposed. The two concepts already applied to non-restoring division are adopted for improving the performance of a non-restoring square root since it has similar process to that of non-restoring division for finding square root. Additionally, a new method to find intermediate quotients is presented that removes an adder per an iteration to reduce the total area and power consumption. The non-restoring square root with MSC generator reduces total delay, area and power consumption significantly.