Xiaoming's clock is 8 am. He went to the library, and the clock in the library just arrived at 8 o'clock.

He borrows books from the library and reads them. When the hand of the big clock points to 1 1, he goes home, which means that he stayed in the library for 1 1-8=3 hours, while Xiaoming's alarm clock went away for 12-8=4 hours.

Xiao Ming's time from home to home = time spent walking from home to the library+time spent in the library for 3 hours (time difference of library clock)+time spent going home from the library.

Because of the same speed, the time from home to the library = the time from the library = 1/2 = 0.5 hours.

Therefore, the time of Xiao Ming's big alarm clock is 0.5 hours later than the accurate time (clock time), and the accurate time for Xiao Ming to get home is 1 1: 30.