How do registers connect to CPU buses
In some device technologies, registers are connected to a bus using three-state outputs.  Such an approach does have some advantages, but it generally either requires that either there be some "dead time" between the moment one register releases the bus and the moment another register starts driving it, or else runs the risk that a device might start driving the bus before the previous device has fully released it.

In other technologies, this approach is avoided in favor of using nested multiplexers.  If there are 64 registers that can output to a bus bit, the device might have eight 8-way multiplexers each of which accepts input from one register, and one more 8-way multiplexer which accepts input from one of the first eight.  While this may use slightly more circuitry than the bus-based approach, it has the advantage that every signal throughout the system will be driven by exactly one device at all times.