Using AT24C02A EEPROM

@DrAzzy I have not decoupling cap, I'm going to buy and apply it.
But I have tried your code without decoupling cap. I think results are good;

>console.log(eeprom.a(eeprom.i2ca)); //check that I2C addressing is being done right
function () { [native code] }
=undefined
>console.log(eeprom.i(0x64)); //check that memory addressing is being done right
80
=undefined
>console.log(eeprom.cap); //sanity check - should be 256 (capacity supplied as kbits, but internally handled in bytes.
256
=undefined
>I2C2.writeTo(0x50,0); //select address 0 manually
=undefined
>I2C2.readFrom(0x50,8); //read 8 characters manually
=[ 255, 255, 255, 255, 255, 255, 255, 255 ]
>I2C2.writeTo(0x50,0x64); //select address 0x64 manually
=undefined
>I2C2.readFrom(0x50,8); //read 8 characters manually
=[ 110, 97, 117, 111, 119, 117, 105, 111 ]
> 

Also I don't know does it care but here is some results about addressing ;

>eeprom.i(2);
=80
>eeprom.i(0x64);
=80
>eeprom.i(0x50);
=80
>eeprom.i(1);
=80
>eeprom.i(0);
=80
> 

One more test result is below, I think it writes and reads when I try manually

>I2C2.writeTo(0x50,0x64);
=undefined
>I2C2.writeTo(0x50,0x64,"MERHABA");
=undefined
>I2C2.writeTo(0x50,0x64);
=undefined
>I2C2.readFrom(0x50,7);
=[ 77, 69, 82, 72, 65, 66, 65 ]