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This paper demonstrates a hafnium zirconium oxide (HZO)-based ferroelectric NEMS unimorph as the fundamental building block for very low-energy capacitive readout in-memory computing. The reported device consists of a 250 $μ$m $\times$ 30 $μ$m unimorph cantilever with 20 nm thick ferroelectric HZO on 1 $μ$m $SiO_2$.Partial ferroelectric switching in HZO achieves analog programmable control of the piezoelectric coefficient ($d_{31}$) which serves as the computational weight for multiply-accumulate (MAC) operations. The displacement of the piezoelectric unimorph was recorded by actuating the device with different input voltages $V_{in}$. The resulting displacement was measured as a function of the ferroelectric programming/poling voltage $V_p$. The slopes of central beam displacement ($δ_{max}$) vs $V_{in}$ were measured to be between 182.9nm/V (for -8 $V_p$) and -90.5nm/V (for 8 $V_p$), demonstrating that $V_p$ can be used to change the direction of motion of the beam. The resultant ($δ_{max}$) from AC actuation is in the range of -18 to 36 nm and is a scaled product of the input voltage and programmed $d_{31}$ (governed by the $V_p$). The multiplication function serves as the fundamental unit for MAC operations with the ferroelectric NEMS unimorph. The displacement from many such beams can be added by summing the capacitance changes, providing a pathway to implement a multi-input and multi-weight neuron. A scaling and fabrication analysis suggests that this device can be CMOS compatible, achieving high in-memory computational throughput.