What is the advantage of 4-20mA analog signal as compared to 0-10V signal? How can you read 4-20mA if your BAS inputs only accept 0-10V?

In addition to what others have mentioned, a current signal is intrinsically high impedance.  What the means in this case is that the length (and therefore the resistance) of the connecting cable has virtually no effect on the signal integrity. 

A 4 mA current injected at the source will produce a 4 mA current flow at the load whether the interconnecting wire has a resistance of 1 ohm or 1000 ohms.  [Assuming the source has sufficient compliance.]

In addition, all else being equal, a current loop will be 'faster' (have a higher frequency response) than a voltage system. 

A 4-20mA current loop AC coupled to a .625Ω resistor will give you a 0-10V signal.

Read Andy's comments.

The primary advantage of using a non-zero low end range (4-20mA vs 0-20mA, 0-10V, etc.) is that this gives you the ability to detect an open circuit. If you're using a 4-20mA signal and yo read significantly less than 4mA then you would know that there is a problem with the signal - a broken wire, failed instrument, loss of loop power, etc. With zero-based ranges you have no easy way of knowing if 0V (or 0mA) is a valid signal or not.

A low power 4-20mA sensor can be powered by its two wire connection.

A 0-10V sensor needs power supply connections in addition to the signal output connections.

To read 4-20mA simply with a 10V input, just connect a 500 Ohm resistor across the input and connect the sensor in series with positive power and positive input, with negative input grounded.

That will give a 2V to 10V input so you need to rescale slightly, but avoids any complex analog circuitry to convert the zero point.