Construct a Hamming code that will correct single bit errors in a 32 bit word. Construct a specific error in a Hamming code output (original 32 bit word plus whatever you must add for Hamming) and explicitly verify that the Hamming correction algorithm first detects and then corrects the error. How many bit errors will your code detect? Construct a specific error in more than this number of bits and explicitly show that the Hamming algorithm fails to detect the error. How space (number of bits required) efficient is your Hamming code?