Q$5.$ Suppose that Coin XYZ uses a $48-$bit hash function to link the blocks, and it has an average block time of $3$ minutes. Assume the current network difficulty is $4$ M$,$ and it is adjusted every $1200$ blocks.

$($a$)$ How many leading zero bits does the target hash have now if the initial target hash of the Genesis Block had $12$ leading zero bits $($the remaining bits are $1\text{'}$s$)?$

$($b$)$ Suppose that more miners join the network. Compute the next difficulty if the total time to mine the last $1000$ blocks was $50$ hours, and find the corresponding next target hash in hex digits.