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This paper describes squaring and square-rooting circuits operable on low voltage supplies, with their application proposed hereby as vector-summation and four-quadrant multiplier circuits. These circuits make use of a flipped voltage follower (FVF) as fundamental circuit. A detail classification of basic topologies derived from the FVF is given. The proposed circuits have simple structure, wide input range and low power consumption as well as small number of devices. All circuits are also examined and supported by a set of simulations with PSpice program. The circuits can operate at power supply of ±0.7 volts, the input voltage range of the squaring circuit is ±0.8 volts with 1.59% relative error and 1.78 μW power dispersion, the input current of the square-rooting circuit is about 50 μA with 0.55% relative error and 1.4 μW power dispersion and the vector-summation circuit have linearity error of 0.23% and 2.92 μW power dispersion. As in four-quadrant multiplier circuit, the total harmonic distortion of the multiplier is less than 1.2% for 0.8 V_P-P input signal at 1 MHz fundamental frequency. Experimental result is carried out to confirm the operation by using commercial CMOS transistor arrays (CD4007). These circuits are highly expected to be effective in further application of the low voltage analog signal processing.

"Vedic mathematics" is the ancient methodology of mathematics which has a unique technique of calculations based on 16 "sutras" (formulae). A Vedic squarer design (ASIC) using such ancient mathematics is presented in this paper. By employing the Vedic mathematics, an (N × N) bit squarer implementation was transformed into just one small squarer (bit length ≪ N) and one adder which reduces the handling of the partial products significantly, owing to high speed operation. Propagation delay and dynamic power consumption of a squarer were minimized significantly through the reduction of partial products. The functionality of these circuits was checked and performance parameters like propagation delay and dynamic power consumption were calculated by spice spectre using 90-nm CMOS technology. The propagation delay of the proposed 64-bit squarer was ~ 16 ns and consumed ~ 6.79 mW power for a layout area of ~ 5.39 mm². By combining Boolean logic with ancient Vedic mathematics, substantial amount of partial products were eliminated that resulted in ~ 12% speed improvement (propagation delay) and ~ 22% reduction in power compared with the mostly used Vedic multiplier (Nikhilam Navatascaramam Dasatah) architecture.