Hi,
I have a board consisting of PIC micro, ADC, DACs etc running on 5V and need to interface the microcontroller with BBB via UART. For 5V-3.3V interfacing, I plan to use this circuit: http://s11.postimg.org/8q2fddr3n/Capture.png
The board gets rectified supply from a transformer. Is it safe to connect the ground terminals of the two devices directly?