Design of a high-speed square generator

Given a binary number N, the simplest way for evaluating its square N² is the use of ROM look-up tables. For example, the squares of 12-bit numbers can be stored in a ROM of (2¹²×24) bits, which takes an area of 3.5 mm² and an access time of 9.96 ns with 0.8 μm CMOS process. However, the conventional ROM table approaches are limited only for small bit size applications due to the unmanageable increase of the ROM table size. A novel design of square generator circuit using a folding approach is presented for high speed performance applications. Results show that, with the same process, the proposed square generator circuit takes 12.27 ns to generate the squares of 40 bit numbers with an area of about 2.88 times that of the (2¹²×24) ROM, i.e., 10 mm² a design trade-off between speed and area. A nested structure is also presented to achieve a 103 bit square generator with a delay of 15.82 ns. The bit size can be further increased by adding more levels of the nested structure. The results are promising and thus the proposed approach is well suitable for large bit size and high speed applications