The Hamming distance between two bit strings is the number of bits that would have to be flipped to make the strings identical.

To **detect d errors** we require a minimum Hamming distance of $d + 1$.

**Correcting d bit** flips requires a minimum Hamming distance of $2\times d + 1,$ where $d$ is number of bit in errors .

**For the first blank**, each error detection we need $1$ parity bit

For $3\ bit$ error detection we need $3$ parity bits. So, $3$ parity bits requires here.

Also, we can calculate this way, formula is $d+p+1 \leq 2^p$ where, $\text{d=data bits , p = parity bits , d=4 bits given}$.

According to $1^{st}$ question, $d=4$ so $4+p+1\leq 2^p$

$p+5 \leq 2^p$ now if p$=2$ it becomes $7 \leq 4,$ Not possible. If $p=3$

It becomes $8\leq 8,$ which is possible.

So, $p$ must be $3.$[ Minimum value of $p$ is $3$ ]

**The second blank** the $3$-bit error detection is possible because the code has a minimum distance of $\underline{\qquad}$answer is $3+1=4,$ where d$=3.$ Formula used is $d+1.$

**Answer for 2 blanks are [ 3,4 ].**