Apply Hamming Code $(HC)$ to the data bits $\text{'}1111\text{'}$ and answer the following questions: $($Hint: $N=2^k-k-$

a$.[6$ pts$]$ Find the encoded bit pattern that is ready for transmission with $HC$ applied to it:

b$.[6$ pts$]$ Assume that an error occurs in the least significant bit. Calculate the syndrome to demonstrate

the error correcting capability of your encoded bit pattern.