Electronic – Is it possible to use 400 kHz I2C buses with a 32 kHz slave

Following up the comments:

Yes, the frequency is hard-coded into some specific I2C-related registers. At runtime.

That said, your Arduino library might be doing some probing and rise time measurement on the bus for determining a viable clock rate. Let's see.

After doing a bit of source-digging, the answer is in twi.h

#ifndef TWI_FREQ
#define TWI_FREQ 100000L
#endif

Another piece from that very file:

TWBR = ((CPU_FREQ / TWI_FREQ) - 16) / 2;

Where TWBR stands for Two Wire Baudrate Register I suspect.

I'd call that enough evidence and definitely say, yes your I2C frequency is set directly by your library without any negotiations. If you want to change it, I'd suggest you #define TWI_FREQ before you #include twi.h (or indirectly through Wire.h)

So in the same situation i want to receive data from a particular slave to a particular master but can the slave start the communication? Like suppose slave is a ADC and once the conversion is done send the converted data to a particular master. Is this possible in I2C?

A device which is a pure I²C slave can not start an I²C transaction. This holds for both multi- and single-master I²C buses.

However, some slave devices can alert the master out of band, not through I²C. When the master sees the alert, it will initiate the transaction. For this purpose, some ADCs have discrete digital outputs which correspond to the state of the A/D conversion. (For example, the AD7998 has got an ALERT/BUSY pin and an I²C connection for readout and configuration.)

If there is a multi-master bus, then a device could switch its role on the fly from master to slave. Then it can initiate an I²C transaction as a master. It would have to be a microcontroller with its own firmware. The vast majority of hard I²C devices are bus slaves, although there are a handful of hard I²C devices that are bus masters. I've never heard of a hard I²C device that would switch from master to slave.

By the way, here's a related thread: https://electronics.stackexchange.com/a/232135 .