Efficient unsigned squarer design techniques

Abstract

Abstract:The partial product matrix (PPM) of a parallel squarer is symmetric. To reduce the depth of PPM, it can be folded, shifted and rearranged. In this paper, we present an efficient unsigned parallel squarer design technique. Also, a fixed-width squarer design method of the proposed squarer is presented. By simulations, it is shown that the proposed squarers lead to up to 18% reduction in area, 10% reduction in propagation delay and 10% reduction in power consumption compared with previous squarers. By using the proposed fixed-width squarers, area, propagation delay and power consumption can be further reduced up to 26%, 15% and 25%, respectively. Keywords: squarer, fixed-width, partial product reduction Classification: Integrated circuits References[1] J. Pihl and E. Aas, "A multiplier and squarer generator for high performance DSP applications,"

Design of an Efficient Combined Unsigned and 2’s Complement Squarer

“…2(b) can be obtained. In order to further reduce the partial product bits of squarers in [4], the addition of 1 − i i a a on column 2i and a i a i-2 and a i-1 a i-2 on column (2i-1), (where i = 2, … , W-1) in Fig. 2(b) can be simplified as…”

“…The folding technique described in [1] uses the symmetry of the partial product matrix of squarer to achieve 50% reduction of the number of partial products compared with a standard multiplier. The partial products rearrangement techniques in [2,3,4] is used to reduce the total number of partial products bits and the depth of partial product matrix.…”

Pipelined Squarer for Unsigned Integers of Up to 12 Bits

“…Most optimization schemes exploit the folding and merging techniques, which use x i + x i = 2x i and x i + x i x i−1 = 2x i x i−1 + x i x i−1 , respectively [2]. Figure 1 describes the use of the optimization techniques in a 4-bit unsigned integer squarer.…”

“…The high-radix techniques [4], [5] or signed-digit techniques [6] can be beneficial but require extra circuits to recode operands or convert representations. The designs with reduced precision, such as in [2], are also interesting but are not considered in the present study.…”