JAJSI83G May 2012 – November 2019 TCA9548A
To write on the I2C bus, the master sends a START condition on the bus with the address of the slave, as well as the last bit (the R/W bit) set to 0, which signifies a write. The slave acknowledges, letting the master know it is ready. After this, the master starts sending the control register data to the slave until the master has sent all the data necessary (which is sometimes only a single byte), and the master terminates the transmission with a STOP condition.
There is no limit to the number of bytes sent, but the last byte sent is what is in the register.
Figure 10 shows an example of writing a single byte to a slave register.