0xFF is the largest value that can be stored in one byte, for signed integers that is 0xFF/2, which is 127.5 (use a calculator if you must). Since you can put 0.5 in a byte, one side is 127 and the other is 128 so that 127+128 = 255 (0xFF).
limits.h contains the upper and lower limits of all numeric data types supported by your compiler.
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