Hashing
Hashing is a technique used for storing and retrieving keys in a rapid manner.
In hashing, a string of characters are transformed into a usually shorter length value or key that represents the original string.
Hashing is used to index and retrieve items in a database because it is faster to find item using shorter hashed key than to find it using the original value.
Hashing can also be defined as a concept of distributing keys in an array called a hash table using a predetermined function called hash function.
A binary tree is a tree with the condition that each node only has a maximum of two subtree and the two subtree must be separate. In accordance with this definition, each node in the binary tree must only have at most two children / children.
In a blockchain, each node of the network stores the full data. So it is absolutely not the same idea as the DHT in which data are divided among nodes. Every new entry in the blockchain must be validated by a process called mining whose details are out of the scope of this answer but this process insure consensus of the data
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