How does an analogue to binary converter work?

The A/Ds in most microcontrollers work a bit at a time (successive approximation). Although they might seem fast, in electronic terms they are relatively slow; if you wanted to digitise video, for example, you'd use a fast flash converter not successive approximation.

When I say 'a bit at a time' I mean that literally. First step is to compare the input with half the reference voltage. If it's higher the most significant bit of the result is 1, if it's lower it's a 0. If the result was 0, the input is compared with half of a half (a quarter) and the result becomes the next bit. If the result was 1 the input is compared with a half plus a half of a half (threequarters). And so on until the result is complete, with each result controlling the next one. If it's a 10-bit A/D there will be 10 steps. In terms of hardware it's conceptually quite simple - a comparator and a way of generating all the levels and switching them to the comparator at the appropriate time. (Simple for a chip designer - if you built one on a breadboard you probably wouldn't want do more than 3 or 4 bits.) If you think about it for a moment, you'll realise that the part that generates the levels is actually a D/A. It's called successive approximation because at each step it's doing a better and better approximation to the result. You could stop part way through and your result would be the right result for the number of bits you'd done. (You can also think of it as being a kind of binary search because there are two outcomes at each step.) As to the exact details of how it's done in a chip, I couldn't tell you.

A simpler (and slower) scheme is to use the comparator and the D/A but just ramp the D/A level until it matches the input, but that takes a variable number of steps (for 10 bits, the average would be 512 steps but it might be as many as 1024). A much faster scheme is to have a comparator for each level (1024 of them for 10 bits) and do all the comparisons at once with encoding logic to generate the binary output from all the outcomes.

The A/Ds in most microcontrollers work a bit at a time (successive approximation). Although they might seem fast, in electronic terms they are relatively slow; if you wanted to digitise video, for example, you'd use a fast flash converter not successive approximation.

When I say 'a bit at a time' I mean that literally. First step is to compare the input with half the reference voltage. If it's higher the most significant bit of the result is 1, if it's lower it's a 0. If the result was 0, the input is compared with half of a half (a quarter) and the result becomes the next bit. If the result was 1 the input is compared with a half plus a half of a half (threequarters). And so on until the result is complete, with each result controlling the next one. If it's a 10-bit A/D there will be 10 steps. In terms of hardware it's conceptually quite simple - a comparator and a way of generating all the levels and switching them to the comparator at the appropriate time. (Simple for a chip designer - if you built one on a breadboard you probably wouldn't want do more than 3 or 4 bits.) If you think about it for a moment, you'll realise that the part that generates the levels is actually a D/A. It's called successive approximation because at each step it's doing a better and better approximation to the result. You could stop part way through and your result would be the right result for the number of bits you'd done. (You can also think of it as being a kind of binary search because there are two outcomes at each step.) As to the exact details of how it's done in a chip, I couldn't tell you.

A simpler (and slower) scheme is to use the comparator and the D/A but just ramp the D/A level until it matches the input, but that takes a variable number of steps (for 10 bits, the average would be 512 steps but it might be as many as 1024). A much faster scheme is to have a comparator for each level (1024 of them for 10 bits) and do all the comparisons at once with encoding logic to generate the binary output from all the outcomes.