There are a couple of different microphone types, mainly dynamic and condenser. I’ll explain the dynamic microphone, as that’s a bit easier to understand.
The dynamic mic is basically the same as a speaker driver, but in reverse. The soundwaves make a membrane vibrate. There is a small coil of very thin copper wire attached to the membrane. When this coil moves near a magnet, a small electric current is induced in the wire, which will follow tje waveform of the soundwaves. This is then taken out of the microphone and amplified.
The conversion from analog to digital happens in a separate unit called a A/D converter. Sometimes it’s built into the microphone (eg. USB microphones)
The A/D converter works by sampling the voltage from the microphone many thousand times per second. 48 000 Hz is a common sampling rate in pro audio. This means that the converter measures the voltage 48 000 times every second and then assigns a binary value to it. If the bit depth is 24 bits, then one sample might be say
101100010011010101110110
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