PC8563 Arduino interface
Normal I2C addresses are 7-bit long. On the first frame of an I2C
transaction, the master sends an 8-bit byte containing the address of
the slave followed by a bit specifying whether this is a read or a write
operation. Some people tend to call “address” the whole 8-bit frame,
which causes confusion. Because of this, we end up having three flavors
of I2C addresses:


the 7-bit address, which is the real device address
the 8-bit “write address”, which is the address followed by a 0
meaning “write operation”
the 8-bit “read address”, which is the address followed by a 1
meaning “read operation”


For your RTC, the 3 addresses are the following, in hex and binary:

7-bit = 0x51 = 0b1010001
write = 0xA2 = 0b10100010
read  = 0xA3 = 0b10100011


The Arduino Wire library expects the 7-bit address.