The idea behind this circuit is to use two transmission-gates as simple switches to propagate either input A or input B directly to the output. The extra inverter generates the inverse of the SEL select input. While the upper transmission-gate is activated by SEL, the lower transmission-gate is activated by !SEL, due to the wiring of their control (gate-) inputs.
When SEL is low, only the lower transmission-gate is conducting (because !SEL is connected to its n-channel and SEL to its p-channel transistor gate inputs), while the upper transmission-gate is non-conducting. As a result, the value of A is passed through to the output of the multiplexer.
When SEL is high, the upper transmission-gate is activated, while the lower transmission-gate is non-conducting. Therefore, the value of B is passed through to the multiplexer output.
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