Efficient Design of Vedic Square Calculator Using Quantum Dot Cellular Automata (QCA)
Angshuman Khan, Ali Newaz Bahar, Rajeev Arya
Abstract
Self-multiplier or square calculator design using the Vedic formulas is the new trend in quantum-dot cellular automata (QCA) technology. However, an efficient coplanar design and a complete performance analysis are still desired. This brief presents the coplanar QCA architecture of a 2-bits square calculator (proposed design-1 or PD1) using the Vedic sutra ‘Urdhva Tiryagbhyam’. Furthermore, based on the E-shaped XOR gate and majority gate (MV) an optimized architecture (proposed design-2 or PD2) is presented. The PD2 architecture exhibits notable improvement compared to the previous architecture. The proposed PD2 requires 17%, 53%, and 25% fewer cells, smaller area, and lower latency, respectively. Likewise, the extended design for 4-bits architecture (proposed design-3 or PD3) achieves 67%, 63%, and 62% superiority in cell count, covered area, and latency, respectively. Compare to the best previous design, the area-delay, QCA-specific, and energy-delay costs for PD2 (PD3) are lower by a factor of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {\mathrm {\sim }}10$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ \mathbf {\mathrm {\sim }}30$ </tex-math></inline-formula> ), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ \mathbf {\mathrm {\sim }}71$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ \mathbf {\mathrm {\sim }}33$ </tex-math></inline-formula> ), and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ \mathbf {\mathrm {\sim }}64$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ \mathbf {\mathrm {\sim }}83$ </tex-math></inline-formula> ), respectively. Moreover, there is an improvement in terms of power dissipation as the QCA based designs PD2 (PD3) dissipates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.41 \mathbf {\mathrm {\times }} 10 ^{-6~}$ </tex-math></inline-formula> mW ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$11.82 \mathbf {\mathrm {\times }} 10 ^{-6}$ </tex-math></inline-formula> mW), whereas the similar type CMOS-based designs dissipate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.29 \mathbf {\mathrm {\times }} 10 ^{-2}$ </tex-math></inline-formula> mW ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$48 \mathbf {\mathrm {\times }} 10 ^{-2}$ </tex-math></inline-formula> mW), respectively. It is worth mentioning that the comprehensive performance analyses are carried out using the QCADesigner, QCADesigner-E, and QCAPro tools.