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Analog-to-Digital conversion is a basic signal processing task that is needed at various places in the context of modern day mixed-signal systems like instrumentation & control systems, system-on-chip, etc. It is because of the fact that most real-world signals are analog in nature whereas most on-chip computation is digital. The technical literature is replete with electronic implementations of analog to digital converters including, but not limited to, Flash ADC, Successive Approximation ADC, and Sigma-Delta ADC. Given their promise of parallel processing and fast convergence, artificial neural networks have also been employed for analog-to-digital conversion. The first such attempt employed the Hopfield Neural Network and later several variants were introduced. However, most of the existing neural circuits for analog-to-digital conversion have an underlying similarity in the sense that they are derived from the Hopfield Network Architecture. A new scheme for analog-to-digital conversion utilizing a neural circuit for solving systems of linear equations is presented. The circuit employs (2n) opamps and (n+3) resistances for an n bit ADC.