How is binary converted to electrical signals?
I want to restate part of KellenJB's answer in a slightly different way:

There is no conversion from binary 1's and 0's to voltages like 5 V and 0 V. The microcontroller, or any physical circuit, just operates on the voltages. 

Those voltages are "converted" to binary 1's and 0's in our heads when we form a simplified model in our minds about how the circuit is working.