MCUs are typically used to interface with the real world, and that world is analog. That means that instead of the binary high and low logic levels, voltages vary smoothly. Digital electronics (which includes MCUs) can't directly work with analog voltages, so they need to quantify such voltages into digital values.

This quantification involves converting the analog signal into a number with some number of bits. As a simplest case example, we could have a 1-bit analog to digital converter. If the analog signal is below half Vcc (2.5 volts for a 5 volt MCU) we could convert it to a low (aka 0), otherwise we could convert it to a high (aka 1). The more bits we convert to, the better the approximation to the actual analog signal.

Measuring light using a photocell is a great example of this. It's a light sensitive resistor that you use in series between Vcc and ground with another resistor. As the strength of the light falling on the photocell changes, so does its resistance, and so does the voltage at the point between it and the other resistor. If we measure that voltage we can get a sense of what the strength of the light is. For example, assume that we're measuring a signal between 0 and 5 v. Let's say our input signal is 2 v. That's 2/5 of Vcc, i.e. 40%. If our ADC is 8-bit (i.e. converts to an 8 bit number) the result would be 102. If it's a 16-bit ADC the result would be 26,214. The more bits in the ADC result, the finer it's resolution, i.e. the less change each increase of 1 in the result indicates (0.195 v for an 8-bit ADC, 0.0000763 v for a 16-bit ADC). 10 or 12 bit ADCs are pretty typical. The '328 has a 10-bit ADC, so it's resolution is 5 v / 1024 = 0.00488 v.

Although the '328 has a single ADC, it has an analog multiplexer providing 6 inputs, one of which can be read at a time. These are similar to the digital multiplexers we've seen in previous parts of this series, but work with analog signals rather than digital ones.

So, if more bits gives you a more accurate measurement, why not have as many as possible? Why 10 bits rather than 16? Have a look at the block diagram below of the '328's analog to digital converter. See that red block labeled "CONVERSION LOGIC"? It outputs a 10-bit value to a digital to analog converter (DAC) (in green). That seems a little backwards.. what's up with that? Well, see how the output of the DAC feeds into comparator (in blue)? The other input to the comparator is the output from the analog multiplexer, i.e. the analog signal being measured. The contents of that conversion logic block is a successive approximation circuit. Its output is converted to an analog signal and compared to the input. The result of that comparison feeds back to improve the next approximation.

What's successive approximation? It's a way to incrementally find an answer by trying a guess, seeing how it works out, then adjusting the guess to get closer to the desired outcome. It's like a game of "getting warmer". Let's say we start at the mid-point of the conversion range. Let's use 2 volts from above as the input signal with the 10-bit converter.

We start with a guess of 512. That converts to 2.5 v which is greater than the input (2 v). That means that the next guess needs to be lower. A straightforward approach is to use a binary search technique: make the next guess 256. That converts to 1.25 v which is less than the 2 v input. The next guess will be 384 which converts to 1.88 v which is still less than the 2 v target. So the next guess will be larger: 448 which is 2.19 v. Now it's too big so the next guess has to be lower: 416 which is 2.03 v. That's getting close but still high. The next guess is 400 (1.95 v). Up for the next guess: 408 (1.99 v). Up a bit more for the next guess: 412 (2.01 v). That's just over the target: down for the next guess of 410 (2.00 v). Bingo. Let's look at what we just did.

512 (2.5v) too high (decrease by 256)

256 (1.25v) too low (increase by 128)

384 (1.88v) too low (increase by 64)

448 (2.19v) too high (decrease by 32)

416 (2.03v) too high (decrease by 16)

400 (1.95v) too low (increase by 8)

406 (1.99v) too low (increase by 4)

412 (2.01v) too high (decrease by 2)

410 (2.00v) just right.

The key is to change the guess each time by decreasing powers or 2. This will gradually converge on the target value. It can take several steps to do that. In fact, in the worst case the number of steps required will be the number of bits in the resolution of the converter. So a 10-bit converter will take 10 steps in the worst case. If the converter has more bits, the worst case conversion time gets longer. That's why we don't just have 16 or 32 bit converters. There's always a trade-off. Always.