I have a project using an ATMEGA328P and a DS1337 RTC chip. The DS1337 is an 8 pin IC with VCC at pin 8 and GND at pin 4. According to the datasheet both pin 5 (SDA) and pin 6 (SCL) need an external pull-up. From what I read elsewhere, a pull-up of 4.7K to 10K for each I2C pin should be good enough. Considering the position of both I2C pins to each other and the VCC pin, I was thinking of simplifying things by using a shared 10K pull-up. This post suggests that it should be possible, but I am still not sure. Does anyone have experience with this, that is using a shared pull-up to an I2C connection? What could be some problems, if any, by doing this?
You need at least one pull-up on the SDA pin and at least one pull-up on the SCL pin. You cannot use the same pull-up for both pins as you will be shorting the two pins together.
The pull-ups are required on the I2C signals, not the pins of a chip. If you have multiple chips on the I2C bus you only need one pull-up on each signal. It really doesn't matter (given that I2C buses are intended to be short) where on the signal the pull-up is in relation to any one chip.
I would personally say that 4.7kΩ to 10kΩ is too high. I don't use more than 3.3kΩ pull-ups for I2C, and more likely 1kΩ if I am using higher speed (e.g., 1MHz) I2C.