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This lecture covers the design of datapath subsystems, focusing on basic combinational components such as decoders, encoders, priority encoders, multiplexers, demultiplexers, magnitude comparators, and shifters. It also delves into the implementation options for adders, including CLA, carry-skip, and carry-save adders, as well as parallel-prefix adders. The lecture explores multiplication algorithms, array multipliers, Booth's algorithm, and Booth's array multipliers. Additionally, it discusses division algorithms, subsystem design using priority encoders, domino logic, and modular design. The lecture concludes with the design of barrel shifters, logical and arithmetic shifts, rotations, and the implementation of counters.