Wiring Question: ground and negative

I am attempting to connect an Eagle Cuda 128 Transducer to an Arduino Uno.

Based off of some wiring diagrams online, I think that the Depth signal is the blue wire, the Temperature signal is the yellow wire, the negative(-) is the black wire, the postive is the white wire, and the ground is the bare wire (seen in the diagram).

The transducer is ran off of a 12v marine grade battery. My question is what do I do with the bare (ground) wire when I connect it to the arduino? Should I also connect the negative cable to the arduino?

Should I use a RS232 converter to change the 12v signal to TTL logic?

My question is what do I do with the bare (ground) wire when I connect it to the arduino? Should I also connect the negative cable to the arduino?

You can but ideally you should connect it to an earth or real ground for maximum screening.

Should I use a RS232 converter to change the 12v signal to TTL logic?

Why, what is the output of your transducer? Transducer outputs are normal analogue not digital.

seen in the diagram

What diagram?

You indicate you are trying to connect the transducer from a Cuda 128 depth sounder to an Arduino. In general, you can't get there - the transducer is expecting a 200khz burst at 800 watts peak (from page 2 of the Users Manual ) which is probably several hundred volts. The return signal may well be quite low level, but that is what the sounder itself handles with an amplifier that looks for that return signal (and is protected from damage from the transmit burst). The difference between the transmit burst and the receive echo determines the depth. There is really no way for the Arduino to generate that sort of signal. As far as the wiring goes, the bare wire is usually a shield on the cable to the transducer.