(2) For 11-bit code words a four subset Venn Diagram could be used to create a 15-bit errorco recting word by placing the 11 digits into the regions a) through k ) and using the regions labeled w,x,y, and z as your error correcting regions. You place a 0 or 1 into these regions so that an even number of 1 's is in each of the four circles. Unlike the previous example when there are seven unique regions for the three circles the four set example has 15 regions total in the four ellipses. a) Verify that the 11-bit word 10011011100 has the 15-bit Hamming code 100110111001010. 11-bit 15-bit b) Correct the one incorrect bit in the 15 -bit Hamming-coded word 001100111100100 . For the words 110011101101101 and 111110000010000 there is at most one incorrect bit. Determine if the word is correct and if the word is not correct change it so that it is correct; explain your reasoning here