Colour depth for certain applications

I am using a 17-inch, Mid 2010 MacBook. I checked what processor I have, and it told me my processor was an Intel Core 2 Duo, and it said in the table at http://support.apple.com/kb/HT3696 that the Intel Core 2 Duo was 64-bit. Now, my question is: even if the processor is 64-bit, does the colour depth of the screen also need to be 64-bit for applications that require a 64-bit processor?