Thousands, if not millions. There are so many that it would be a major task to catalog them all. They could be categorized by technology used or by function.
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integrated circuit
when solder IC chips on printed circuit cards
IC stand for Integrated Circuit, so all microcontrollers is IC's but not all IC's is microcontrollers. There is millions of IC types with different porpoises some is microprocessors some is microcontrollers but most IC's has other functions like Oppamps, timers, logic gates, regulator ETC.
That depends on what type of IC you're asking about. IC stands for Integrated Circuit, meaning that the circuit can have quite a number of components. Basically, they are composed of miniaturized transistors that have been manufactured in such a way as to create a circuit that performs a specific function. If you want a buffer that accepts a stream of data and stores it until it is called for by a micro-controller, there are IC circuits that do that. Many transistors are combined in a way that functionally creates a set of J-K flip-flops or equivalent memory units, a counter is created that points to where the NEXT data bit should be stored, and peripheral circuitry is included to allow for reading and clearing the data. It's all performed at the sub-miniature level and in such a way as to allow it all to be on a single chip. Different IC chips will have different requirements, and as such will be designed in a completely different way with unique internal circuitry. The IC industry is not a simple technology, and as such will require quite a bit of education in math, electronics and physics to understand.
Its not about size, its about controls. If the unit has a control board with IC chips, it uses a glow plug. If it uses mechanical switches, as most older units do, it will have a pilot.