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This lecture discusses the design and functionality of multiplexers, specifically focusing on 2-to-1 and 1-to-2 multiplexers. The instructor begins by solving an exercise on a 2-to-1 multiplexer, explaining the concept of control signals and their role in determining the output. The lecture details how the control signal S and its inverse S bar are applied to two inverters, leading to the output based on the state of S. When S equals 0, the output corresponds to signal B, while when S equals 1, the output corresponds to signal A. The instructor highlights the number of transistors used in the design, noting that a typical 2-to-1 multiplexer requires 12 transistors. The lecture also introduces the concept of transmission gates as a means to reduce the number of transistors to 8. The instructor further explains the truth table for the multiplexer, demonstrating its operation and discussing the implications of removing isolation in the circuit design.