Here is a photo of the inside of one integrated circuit.
http://static.righto.com/images/741/clean_scaled_small.png
This is a very early integrated circuit from the 1950s, the ua741 operational amplifier. It is a purely analog circuit, which essentially is an amalgamation of about 25 transistors and a couple of diodes, resistors and capacitors in a package which is much smaller than could have been done using conventional circuit board construction of the time. So this is about as simple as it gets.
A modern integrated circuit will usually have anywhere from 10 times to 1 million times that many transistors. This is a modern ARM micro controller: https://upload.wikimedia.org/wikipedia/commons/thumb/8/89/STM32F103VGT6-HD.jpg/1200px-STM32F103VGT6-HD.jpg Its manufacturer does not specify the exact number of transistors, but given that it has 96 kB of SRAM and 1MB of Flash memory, it is certainly in the millions. Most likely all of the business of the ARM Cortex-M3 core is in the bottom left corner where you have pink and green colors, and the other 85% of the chip is either RAM or Flash.
Around the edge of that Cortex-M3 die you can see square pads (purple on a yellow border). These are the bond pads, which are welded to a frame, which in turn is soldered to the circuit board.
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