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Ising computation is an emerging paradigm for efficiently solving the time-consuming Combinatorial Optimization problems (COP). In particular, Compute-In-Memory (CIM) based Ising machines are promising for Hamiltonian computations capturing the spin state dynamics using a dense memory array. However, the advancement of CIM-based Ising machines for accurately solving complex COPs is limited by the lack of full spin-connectivity, small bitwidths of the spin interaction coefficients (J), data movement energy costs within the CIM, and the area/energy overheads of peripheral CIM analog circuits. In this work, we present a data movement-aware, CIM-based Ising machine for efficiently solving COPs. The unique design contributions are: (i) “Ping-Pong” transpose array architecture restricting single-bit spin data movement within the memory array while maintaining interaction coefficients (J) stationary, (ii) Fully connected spins and multi-bit J for >329× faster solution time, (iii) Configurable J bit-widths and spin connectivity to support wide variety of complex COPs. (iv) Bitcell-Reference (BR) based capacitor-bank-less ADC for sensing, occupying 1.81× less area than the baseline SAR ADC. The silicon prototype in 65 nm CMOS demonstrates >4.7× better power efficiency, and >9.8× better area efficiency compared to prior works.