Design and implementation of an area and time efficient systolic parallel Booth multiplier

Abstract

This paper presents combined area-efficient and time-efficient systolic architectures for parallel Booth multiplication. These systolic architectures employ composite (instead of fine grained) cells in order to optimize the silicon area and latency. The complexity of the composite cell is controllable by choosing the proper input size. The composite cell design takes advantages of algorithmic improvements within the cell. These cells are connected only to the neighbors. IntroductionRecent advancements in IC fabrication technology with respect to the reduction in minimum feature size, enlargement in chip size, and improvement in packing efficiency have made it feasible to put millions of transistors in a single chip. Miniaturization of MOS transistor dimensions continues to improve the circuit speed and packing density, whereas interconnection capacitance and resistance increases linearly with respect to the scaling factor. With increasing chip dimensions, parasitic interconnection capacitance dominates the gate capacitance, and hence RC time consrant of interconnection determines the circuit performance. Such factors become predominant particularly in ULSI technology. For ULSI environments, a new design philosophy locally long but globally short interconnections has been proposed in [1][2], which permits a complex (composite) cell design rather than a fine grained cell for systolic architectures. This paper exploits the concept to modified Booth parallel multiplication. The direct implementation of multiplication using shift-and-add parallel array requires O(n2) silicon area and 3n -2 cell delays for ann x n multiplication [3], each cell consists of a carry save adder, AND gate and data latches.A bit-parallel systolic array has been proposed for multiplication by McCanny and McWhirter[4]. It consists a diamond-shape array of n2 latched carry save adder cells. Each cell is connected to the nearest neighbors, but required 3n clock cycles. A one dimensional serial systolic multiplier array has been proposed for modified Booth implementation [5]. It consists of n/2 cells but each cell contains a ripple carry adder, and it requires 2n -1 clock cycles. A recent floating-point design exploits modified Booth algorithm using Wallace tree reduction and Dadda parallel counter [61.In this paper, we present a novel area and time efficient systolic parallel modified Booth multiplier. A suitable computational model for ULSI has been adopted from the existing VLSI models. Taking wire delays and cell delays into account, we propose systolic architectures with complex cells, which require less area and latency as compared to the fine grained implementation. The complex cell design enables to take advantage of the developments in parallel multiplier, which improves of the cell. Then we show our design approach is viable and results in an area and time efficient implementation. 2.Scaling MOS transistor reduces the dimensions of a device as well as increasing its speed. On the other hand, for interconnections RC constant per unit len...