Vedic-Based Squarers with High Performance

Squaring operation represents a vital operation in various applications involving image processing, rectangular to polar coordinate conversion, and many other applications. For its importance, a novel design for a 6-bit squarer basing on the Vedic multiplier (VM) is offered in this work. The squarer design utilizes dedicated 3-bit squarer modules, a (3*3) VM, and an improved Brent-Kung Carry-Select Adder (IBK-CSLA) with the amended design of XOR gate to perform fast partial-products addition. The 6-bit squarer circuit can readily be expanded for larger sizes such as 12-bit and 24-bit numbers which are useful for squaring the mantissa part of  32-bit floating-point numbers. The paper also offers three architectures for 24- bit squarer using pipelining concept used in various stages. All these squaring circuits are designed in VHDL and implemented by Xilinx ISE13.2 and FPGA. The synthesis results reveal that the offered 6-bit, 12- bit, and 24- bit squarer circuits introduce eminent outcomes in terms of delay and area when utilizing IBK-CSLA with amended XOR gate. Also, it is found that the three architectures of 24- bit squarer present dissimilar delay and area, and the architecture design based on 3-bit squarer modules with  (3*3) VM introduces the lowest area and delay