The I2CRead command will simply grab the content of each Register.

With the DS1307, you find that bit 7 in some of the registers is used for odd things. So, stripping that out, the first four bits (0-3) is the units digit (in binary), and bits 4-6 is the tens digit (in Binary). Which is why they fiendishly called it Binary Coded Decimal.

You've noticed it's in BCD. The first thing is to convert it to something that is useable. So I end up with a single variable that is HOURS, another variable for MINUTES etc. It's easier to have a single byte whose content varies from 0 (zero) to 59 representing MINUTES, because then you can perform math on it directly.

If your Alarm time is stored in the PIC (say your morning alarm at 07 Hours and 15 Minutes) it's a simple matter to compare if those two variables (say ALARMHour and ALARMMinute) match what you've read from the RTC (after converting from BCD). I tend to ignore seconds because unless you're polling better than once a second (or have a hardware interrupt on receipt of the SQUARE wave the RTC can output), or if your code is sloppy, you can easily miss one second.

If you're really clever, you can convert the Date and Time to JULIAN Date & Time, which gives you a single variable which holds a linear combination of Year, Month, Day, Hour, Minute and Second. Now this is great, because then you can simply add 3600 to advance an hour etc etc. There's another thread somewhere on this forum where I did just that with another DS series chip (albeit some years ago). This is the method I choose to use for things like Alarms with a DATE attached (eg Central Heating Timers), whereas Alarms with just TIME (such as your bedside radio's) usually comparing Hours and Minutes suffices.