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Current monitor monitors low voltage spply current?

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Look here https://en.wikipedia.org/wiki/Current-to-voltage_converter Figure 13. Thisis your basic current to voltage converter. It's output is Vout = -I*Rf.

If you add a voltage reference at the non inverting input, te output becomes Vout - Vref-I*Rf

So, you basically level shift the output with the 1.25V reference. The output is +-128 mV typically so you get an output range of 1.25-.0.128 to 1.25+0.128.
 
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