Loss of Precision, example

As an example, consider the 32 bits binary number

$$ (10111110111101000000000000000000)_2, $$ where the first bit is reserved for the sign, 1 in this case yielding a negative sign. The exponent \( m \) is given by the next 8 binary numbers \( 01111101 \) resulting in 125 in the decimal system.