Hello steemians how are you? I hope you all are fit and fine in this pandemic time. Today I read season 3 lectures of the crypto academy and I found it a really interesting and creative way to increase quality content and knowledge.

Today professor @pelon53 explain a wonderful lecture on Hash Root and Merkle Tree. After complete analysis and reading now I am submitting my homework post to professor.

HOMEWORK by @rinkisaxena

Question 1:-

Explain in detail the hash root.

Answer 1:-

The speed at which any given mining machine operate is known as a hash rate. In Crypto world block are find by solving Complex computational problems that are considered to be the mathematical puzzles. All these blocks are hidden in mathematical puzzles. Every second mining machines make more than thousand of guesses to find the correct block. The first who solve will get the block and that speed is known as the hash rate.

For example if a machine is mining Bitcoin and it has rate is very high then it is considered to be more powerful and can easily find mining block on blockchain. This hash rate technology is very much useful for the cryptocurrency project that work on proof of work consensus algorithm. Hash rate is only telling about the speed of mining. Its actual SI unit is Hash/second but as the power increase the unit changes in many different units as shown below:

SI unit	numerical value
1H/S	1
1KH/S	1000
1MH/S	1000000
1GH/S	1000000000
1TH/S	1000000000000
1PH/S	1000000000000000

More the hair straight more will be the power of mining.
Let us see the Bitcoin network has rate to make our idea of hashrate more clear.
By 20th July 2021, hash rate of Bitcoin network is 82.92M TH/S.

We talk about hash rate but the question arises that why it is important to see hash rate ?
So the reasons of checking hash rate is :

• provide information about the strength of the blockchain network.
• more the hash rate refers that more the number of users joining the project.
• it strength it's security.

Show the good hash rate it will make a secure and user-friendly or miner friendly environment with honest miners.

Whenever the new data is added in a new block always mining machine use hash rate that is the computational power to generate new hashes that are the alphanumeric codes that is somewhere equal to targeted hash. This process is accomplished by changing a single value that is known as nounce.

This is the brief information about hash rate.

Question 2:

Make the following Merkle Tree: Transaction (tree leaves): Steem1; Steem2; Steem3; Steem4; Steem5; Steem6; Steem7; Steem8, Made it to the Root Hash. And put every hash generated using SHA-256 , show screenshots, Tell the steps to follow to verify if Steem6 is included in the Markle Tree.

Answer 2:

To create Merkle tree of the given leaves we are using the platform https://xorbin.com/tools/sha256-hash-calculator.

Merkle tree is an essential part of block-chain Technology with which it in sure security and efficiency off the blockchain. It contain hash codes in a form of tree.

In the given question we have to create a tree E with the leaves named as :
Steem1, Steem2, Steem3, Steem4, Steem5, Steem6, Steem7, Steem8

So let us create the hash of each leaf and complete our tree with hash codes.

• Type Steem1 on SHA-256 and calculate hash you will get code as:
  7760e25bcb80adf1dd92db339bf5790a59e90cd54efa072f1250dce13fa97045
  

• Type Steem2 on SHA-256 and calculate hash you will get code as:
  fe00506e91cf52bc4b35321e6b978d1a7349397b19c6c1c01e095971fdec9741
  

• Type Steem3 on SHA-256 and calculate hash you will get code as:
  a9418332e0c351d6a50c835aa9e57d514f0573c231d491e97726db8a5844f2dc
  

• Type Steem4 on SHA-256 and calculate hash you will get code as:
  22f4ec8e20c9ccaf2c313b23f18981b1c73bf39081bcd739e5d998a95a46ab30
  

• Type Steem5 on SHA-256 and calculate hash you will get code as:
  2a3c87336683ab0ddfa56afefc740e6c13a02fea0a43d6797343b26d7af0c57b
  

• Type Steem6 on SHA-256 and calculate hash you will get code as:
  a7baa6de0c0658e9e3681966e542bacd116529f5ae9a2d9126cdb1c1d5bc1278
  

• Type Steem7 on SHA-256 and calculate hash you will get code as:
  d441688dda7f9285e8811728dd9a3955cf74f0a3c7600c1589d0f1d3b48ffac7
  

• Type Steem8 on SHA-256 and calculate hash you will get code as:
  f2e38ed4ff662087b6e9beafa4158ebc488b995732057bda019a6a77ffb5f9f5
  

• The Lower layer of merkle tree is now complete and shown below:
  

• Type Steem1Steem2 on SHA-256 and calculate hash you will get code as:
  a5568957014f6ac3866923c7de20d375e706b8d8c9f453636e90b9965abec62b
  

• Type Steem3Steem4 on SHA-256 and calculate hash you will get code as:
  18d25196db699f6ab9222b7302eb8a6f6ebfadec703c07dd5db8d9455913a499
  

• Type Steem5Steem6 on SHA-256 and calculate hash you will get code as:
  d118e137f92a0dbea138b6bf70c7714153a7bc393cd0272a44bd94864645224b
  

• Type Steem7Steem8 on SHA-256 and calculate hash you will get code as:
  a81d57ba11aedfa9efbba42f6523d75d1efa50b22c5e3557a21ceffe87ddfc4a
  

• The second layer of merkle tree is now complete and shown below:
  

• Type Steem1Steem2Steem3Steem4 on SHA-256 and calculate hash you will get code as:
  8a248c05e69c4f1aa403ad18a7f445ff500c42483da425ce0c980cdb2fd1ad9b
  

• Type Steem5Steem6Steem7Steem8 on SHA-256 and calculate hash you will get code as:
  8b0935aeab3f51bfa2b0750703ee2387e2b20eb19b0d24227e180c03a851af17
  

• Third layer of Merkle tree is completed and shown below:
  

• Type Steem1Steem2Steem3Steem4Steem5Steem6Steem7Steem8 on SHA-256 and calculate hash you will get code as:
  9c2fc83f36d59b8ed5033d2bcc417728583c8daa0aa9868fd374be3619d6e4f9
  

• The final merkle tree is now complete and shown below :
  

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the steps to follow to verify if Steem6 is included in the Markle Tree are follow as :
For this assurance we only need to download aur check the route hash that is the longest hash. To check that we have to follow simple steps :

• Calculate hash Steem5.
  

• Then Calculate Hash Steem7Steem8, Steem1Steem2Steem3Steem4.
  
  

• Now calculate Steem6.
  

• Now combine Steem5Steem6 and calculate its hash.
  

• Now finally Calculate the root hash that is
  Steem1Steem2Steem3Steem4Steem5Steem6Steem7Steem8.
  

• After checking the last hash it is now clear that it is a root hash of the merkle tree.

• And by this we can say that Steem6 is included in the Merkle tree of Steem leaves.

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This is how we have to verify the transaction in merkle tree without checking the whole tree simply download the root hash and verify every node by calculating the root hash.

Question 3:-

Using The SHA-256, You must Place each Complete Hash in The Merkle Tree Transaction (Tree Leaves): SCA1, SCA2, SCA3, SCA4, SCA5, SCA6, SCA7, SCA8. Explain each Step, Show Screenshots. If The Number of Leaves on The Tree is Odd, What should you do? Explain.

Answer 3:-

To create Merkle tree of the given leaves we are using the platform https://xorbin.com/tools/sha256-hash-calculator.

Merkle tree is an essential part of block-chain Technology with which it in sure security and efficiency off the blockchain. It contain hash codes in a form of tree.

In the given question we have to create a tree E with the leaves named as :
SCA1, SCA2, SCA3, SCA4, SCA5, SCA6, SCA7, SCA8

So let us create the hash of each leaf and complete our tree with hash codes.

• Type SCA1 on SHA-256 and calculate hash you will get code as:
  13e0a04bb0e669e1c638dbe3a704743f99f162b25245e4d8c064d35ba38fa8c8
  

• Type SCA2 on SHA-256 and calculate hash you will get code as:
  27849353a9c8cc4e948eb6e5748edd79cb83513d8c0adaf3e8c83d3792c9149b
  

• Type SCA3 on SHA-256 and calculate hash you will get code as:
  67e872f952c105c35e0bce130536d061f4999dca5593754ba9ba7be59b8e7c0d
  

• Type SCA4 on SHA-256 and calculate hash you will get code as:
  491928a32bae70a12fa251412bbfd7c9999f317ba6bf577c283c724225270a43
  

• Type SCA5 on SHA-256 and calculate hash you will get code as:
  99c078c39cde7f47799e0e8691460a9f3e83e78d498ea989308fcfcc58907b19
  

• Type SCA6 on SHA-256 and calculate hash you will get code as:
  7a648d887b124db14e96e23ba92783e7f26d00957c19b9b8229632c2c1873729
  

• Type SCA7 on SHA-256 and calculate hash you will get code as:
  7e0bbd6ba4ba9896f9911af46b06dd2c47535f9c80b29d693fdf6b9319d0d68e
  

• Type SCA8 on SHA-256 and calculate hash you will get code as:
  562abceeb497e1fe7ae275a883fd5ef9d92a05f5c19d82abaa0dc1571b7df3ad
  

• Type SCA1SCA2 on SHA-256 and calculate hash you will get code as:
  91b09bba815748166fb36413342c7e4e7e809f4bac538c0418841a4476b527ef
  

• Type SCA3SCA4 on SHA-256 and calculate hash you will get code as:
  b49b48697a3acbc5e3d2e36b6ee49c44020d88e664c5c1aa7a7cf34058177379
  

• Type SCA5SCA6 on SHA-256 and calculate hash you will get code as:
  f026924cd1285ff92c2a2de9b9313027eb67273a82375c939348c887f6b52f77
  

• Type SCA7SCA8 on SHA-256 and calculate hash you will get code as:
  aa55ec5a6b11393b289c4b2b6916172acc2941c5c978fb1d7bf02696bab323a4
  

• Type SCA1SCA2SCA3SCA4 on SHA-256 and calculate hash you will get code as:
  f50dc120cbf6c46923037f6d7f41d4153ecc9ab7430dda662c142db1ffe483f7
  

• Type SCA5SCA6SCA7SCA8 on SHA-256 and calculate hash you will get code as:
  a3d8ca8494cc426abd5e1fc5fa0feae4f2b2ece4c4cecdca05e19eb66542533f
  

• Type SCA1SCA2SCA3SCA4SCA5SCA6SCA7SCA8 on SHA-256 and calculate hash you will get code as:
  cb40ca6db72dd507cf9118963f94b7740822258e74afb0fd45d89db35d24b386
  

• The final Merkel Tree ia shown below :
  

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This is how we have to create the markel tree. The last line are the leave the middle are the branches and the top has is known as the root hash.

Now the question is what will happen if the number of leaves on the tree are odd in number. So in that case it will be create a duplicate pair of transaction which will complete the whole markle tree. The last transaction in odd number will get duplicated to create a even merkle tree. Let us see an example how how this will happen in odd pair of transactions.

Odd number of leaves.

Let us take an example A1,A2,A3,A4,A5,A6,A7 that means there are in total 7 transaction or 7 leaves in the Merkle tree.

Generated Hash codes are :-

• Type A1 on SHA-256 and calculate hash you will get code as:
  16a36e86f6fed5d465ff332511a0ce1a863b55d364b25a7cdaa25db19abf9648
  

• Type A2 on SHA-256 and calculate hash you will get code as:
  c8361f9b468e68c86da024270e0949ce139cb704b8d7cce586681b99f3a7ea56
  

• Type A3 on SHA-256 and calculate hash you will get code as:
  1398b376fdcce25c5a5399367e76891e85121c010ec919cc243b1a519d95bbc6
  

• Type A4 on SHA-256 and calculate hash you will get code as:
  4e808094851fc2eac7a386fc7d64677b34bda5e41d366ec4943233f9e6f2cd63
  

• Type A5 on SHA-256 and calculate hash you will get code as:
  ea644b359f0b0abde72ab7dbdc03c7d630537bdd0fd7ca1bbb99d41e7f446eea
  

• Type A6 on SHA-256 and calculate hash you will get code as:
  d94791a85f88d5f49c3cc06d5557316cf743d60149820c594f389a1b301ff021
  

• Type A7 on SHA-256 and calculate hash you will get code as:
  724f7bdf7e74a5fe64337203fb8b6ccf4adfc2919665e67a81f02e81752c1c97
  

• Type A1A2 on SHA-256 and calculate hash you will get code as:
  715a38a9be8f0bb3228fbff6b26bf6112513c4c8607bb944c3945e2149e392de
  

• Type A3A4 on SHA-256 and calculate hash you will get code as:
  3d348c69c3dbd0eaa92764e925bbb6e542a1625cf48584ad17bd7805b628977c
  

• Type A5A6 on SHA-256 and calculate hash you will get code as:
  880eaa1f0d20d8d6dae8a7413eae29953d3f53ad41b14ee9d60b99a22441f1b8
  

• Type A7A7 on SHA-256 and calculate hash you will get code as:
  b07f94e8e359222467606be7c7e25bd7ce52d4101cf588cc0671e35e7dbee31b
  

• Type A1A2A3A4 on SHA-256 and calculate hash you will get code as:
  9983e68d41738bcf03fd59001d4e88d7f6d84f9cc6ee03c48785f4701919719e
  

• Type A5A6A7A7 on SHA-256 and calculate hash you will get code as:
  075ae2f1f018c9597b88a6f4bdf8fad0bcdbee5920fa503fb1af484772906a84
  

• Type A1A2A3A4A5A6A7A7 on SHA-256 and calculate hash you will get code as:
  6f9cc0b3e9d846512404388659f80cb12cfc6514dfffa26d10b4e2d7dd0dfb90
  

• The final merkle tree of odd number of transactions is :
  
  The last odd transaction create a duplicate pair name as A7.

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So when there is a odd number of transaction then the last odd transaction will create a duplicate pair that we can see and because of this our Merkle tree form set of even transactions.

Conclusion

Now it's time to conclude our homework post, in this post we discuss about hash rate and merkle tree. The speed at which any given mining machine operate is known as hashrate. In Crypto world block are solved or blocks are hidden in computational Complex mathematical puzzles which one have to solve and get a new block. Hashrate improve and strengthen the blockchain network and create security.Merkle tree is an essential part of block-chain Technology with which it in sure security and efficiency off the blockchain. It contain hash codes in a form of tree. We create to merkle tree of even transactions and also verify how to see single transaction and what happen when the transaction are odd in number. When there is a odd number of transaction then a duplicate block of last order transaction will formed which create and even merkle tree.

THANKYOU SO MUCH