The performance optimization of high-speed arithmetics using the vedic urdhva-tiryagbhyam sutra

Multiplication is a fundamental operation governing the computational throughput of Digital Signal Processing (DSP) architectures, microprocessors, and Finite Impulse Response (FIR) filtering applications. Traditional arithmetic multiplication techniques—such as Array, Booth, and Wallace Tree multipliers—suffer from propagation delays that scale poorly with increasing bit lengths due to sequential partial product generation. This paper presents a high-efficiency alternative based on the Urdhva-Tiryagbhyam (Vertically and Crosswise) sutra derived from ancient Indian Vedic Mathematics. We investigate the underlying mathematical framework for both decimal and binary number systems, illustrate stepwise implementations through multi-digit examples, and detail its mapping onto high-speed Very Large Scale Integration (VLSI) architectures. By restructuring partial product generation to occur synchronously and a priori to the final addition step, this approach inherently minimizes switching activity, reduces critical path delay, and saves dynamic power consumption. Hardware optimizations using Carry-Save Adders (CSA) and compressor circuits are evaluated. Synthesis and simulation parameters validate that the Urdhva-Tiryagbhyam framework yields an area-time-power improvement of approximately 25% to 40% over conventional design practices, positioning it as an ideal candidate for next-generation, high-performance computing hardware.