The conventional computing platforms based on von-Neumann architecture are highly space- and energy-intensive while handling the emerging applications such as AI, ML, and big data. To overcome the von Neumann bottleneck, compact and light-weight logic-inmemory implementations of Boolean logic gates based on emerging non-volatile memory (e-NVM) such as RRAMs, PCM, STT-MRAMs, etc., were proposed recently. However, these e-NVMs not only exhibit significant temporal and spatial variability, but their large-scale integration with CMOS process is also a technological challenge. To overcome these issues with the emerging non-volatile memories, Ferroelectric FETs based on CMOS-compatible doped Hafnium oxide with the capability of large-scale CMOS integration in the advanced logic nodes were proposed. Considering the high scalability and CMOS-compatibility of the FeFETs, in this work, for the first time, we propose a logic-inmemory implementation utilizing a single ferroelectric fullydepleted-silicon-on-insulator (Fe-FDSOI) FET exploiting the unique drain erase phenomenon. In our proposed logicin-memory implementation, inputs are applied at the gate and drain terminals using a novel input-to-voltage mapping scheme, and output is obtained as the current flowing through the Fe-FDSOI FET. We utilize an experimentally calibrated compact model of the ferroelectric capacitor connected to the baseline industry standard BSIM-IMG compact model for the FDSOI transistor for proof of concept demonstration. We also perform a comprehensive analysis of the performance metrics of the proposed logic-inmemory implementation. Our results indicate that we can realize at least 10 Boolean logic gates with high energy and area-efficiency utilizing the proposed scheme.