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...but you generally won't be able to achieve the rail voltages for the ouput. 0 and 5 V are both unabtainable. You can get close like your results.
read the data of a flowmeter (Dynasonics TFXL) and an ultrasonic level sensor (FlowLine DL24). Both units transmit a 4-20mA signal.
The FlowLine DL24 sensor works from 0.1 to 3m.
Its resolution is 1 mm so the A/D converter must be 3/0.001: 3000 ~ 4096 = 12 bits. The ADS1015 converter could work.