Electronic – Trying to understand negative voltages

Looking at your photo, you seem to have +Vs of the LM35 connected to +5V on the Arduino, so if you are reading 3.84V there, that is definitely a problem to address before trying to fix anything else.

The likely problem is this: Te 7 segment displays (or some wiring fault on the breadboard) is drawing too much current from the Arduino, and ultimately from the USB connector. This means that the voltage regulation provided by the USB power supply is no longer working effectively, and so the supply voltage that you measured as 3.84V is likely wandering, and in any case low.

While many if not all the chips in this project will operate off voltages lower than the 5V that V+ is supposed to be at, there are some aspects that will be sensitive to lower V+.

One notable V+ -sensitive feature is the A-to-D convertor in the Atmega328. (As The Photon commented.) The convertor can be set to choose between a couple of different reference voltages. Your code indicates that you have it set to use the V+ (VCC) value (5V) as the reference. If that reference is low (eg: 3.8V) then your input voltage from the LM35 will measure as a number that is scaled up accordingly.

And I'm fairly certain that if your V+ is low, it will change according to how many LEDs are illuminated and drawing current, so your measurements will vary according to what digits are displaying, and vice versa, of course.

Once you've fixed the power supply issue, you might assess whether to set the A/D convertor to use the built-in 1.1V reference instead, as this will give you higher resolution and more stable converted values. See the Atmega328 docs for more details on the A/D convertor and options.

The reality is that you most likely did fry it. We can think about it this way: you supplied much more voltage to it than it was designed to handle, and now it doesn't respond to your computer. What other possibility is there?

The question now is: what exactly did you fry? One thing that could very well be toasted is the ATmega328 chip. Whether you are in luck or not depends largely on whether you have an UNO with the SMD chip or the DIP ATmega328. If it is the former, and the chip is dead then you'll need to get a new Uno, unless you have advanced soldering equipment. If it is the latter you can buy a new ATmega328PU and replace it in your Uno, however, even in this case the solution isn't necessarily easy.

The problem is that you'll need to get a bootloader onto your new ATmega328PU, and without an Arduino or an ISP programmer this isn't easy to do. Fortunately, ATmega328PU with bootloaders already on them are sold on ebay for just a few more dollars than the bare ATmega328PU which runs about $3-$4.

It could also be the case that other (non-MCU) components are damaged either instead of, or (worse) in addition to the MCU: the USB interface chip, voltage regulators, or any of the many passive components that are directly connected to the +5 rail. The trouble is that even with a multimeter it may be difficult to assess the damage. For my money, the best option is to buy a new Uno and move on, however, if you are interested in a (potentially complicated) project, at least the schematics are available. So you would want to look at the schematic drawing and test at least every component that is connected to +5 and ground. Then you might want to test every component connected to those components, in case the blown out component shorted out something else. In the end you might have to test everything.

The alternative strategy would be to assume the best, and look, and maybe try to smell the damage, and replace one or two components that look suspect, and then pray for the best.