Lec-30: Hamming Code for Error Detection & Correction both with easiest examples

Hamming codes are used to detect and correct errors in transmitted or stored data. They are particularly effective at correcting single-bit errors and detecting certain types of multiple-bit errors. Hamming codes add additional parity bits to the original data to enable error detection and correction.

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[shwetasharma]

Sir, please redo this on white board.

[VijendraSingh-bpsf]

Please teach on white board it will extremely helpful and you explained more clear than on digital board🙏🙏🙏

[Malikyuvaan]

Sir this is the first video of yours I didn’t get is seriously

[anushakorla]

Sir, please teach us only on board, we are finding difficult to understand while your are teaching by this digital method🥺.Anyway we love your teaching❤️😌

[relentlessrock]

I'm loving the series. This is the first video where I failed to understand how Parity value was being extracted. Hoping, someone can share some clarity in a reply.

[jaybisht]

For those who failed to understand how Parity value was being extracted and set.

Each redundant bit, ri, is calculated as the parity, generally even parity, based upon its bit position. It covers all bit positions whose binary representation includes a 1 in the ith position except the position of ri. Thus −

---r1 is the parity bit for all data bits in positions whose binary representation includes a 1 in the least significant position excluding 1 (3, 5, 7, 9, 11 and so on)

---r2 is the parity bit for all data bits in positions whose binary representation includes a 1 in the position 2 from right except 2 (3, 6, 7, 10, 11 and so on)

---r3 is the parity bit for all data bits in positions whose binary representation includes a 1 in the position 3 from right except 4 (5-7, 12-15, 20-23 and so on)

[encryptedcicada]

Number of parity bits in the final code: lowest possible value of n that satisfies [ 2^n >= no. of bits in codeword ]
Parity bits location in codeword = 2^n where n starts from 0 (go until the position value exceeds the number of bits in codeword)

Finding the value of parity bits works in this way:

- Take the position number of the parity bit, for example 2 as p1's position is 2.
- We will write down the identifiers of 2 bits and then skip two bits and write down the id of the next 2 bits. In our example we will write down p1 & d0 then skip over 2 ids which are p2 & d1 then we write down next 2 which are d2 and d3. (For position number n will accept n skip n accept n skip n and so forth till the end, including the postion of the parity bits of course.)
We now have the following identifiers with us now: p1 d0 d2 and d3
- We now remove the parity bit ids and xor the remaining data bits, in our case those are: d0, d2, d3. Hence p1 = d0 XOR d2 XOR d3

- If we were to calculate for p2 which is at position 4, we will accept 4 skip 4 accept 4 skip 4 and so forth till the end. In that case we will have the following ids: p2 d1 d2 and d3
- Now we remove parity bit ids and xor the remaining. Hence, p2 = d1 XOR d2 XOR d3

[acquireskills]

Very well explained, but it would be good if explained with white board

[faisalkhan]

VERY NICE, ITS WOULD BE AWESOME IF YOU COULD UPLOAD A PLAYLIST ON C++ PROGRAMMING (theoretical and practical with A-z compiler demo ). YOUR TEACHING METHOD IS AWESOME.

[priyankakhandelwal]

Yes ...plz reupload this video on white board....otherwise your teaching technique is awesome.

[aqsakanwal]

Sir Jo lecture ap deliver krtay hey bht hi helpful thanks a lot for your time and effort # love from Pakistan

[hometvfirestick]

I am continue with his channel for last 4-5 days because my are coming after a week
few minutes ago I was watching COA playlist and this notification comes
your explanation is amazing it helps me alot to understand these terms very easily.

[dkbagdi]

I am following this course. all your lectures are amazing but everything you taught on the digital screen is kinda confusing. for me, it's hard to understand. when you use a marker and whiteboard we can see your hands moving. but on this screen, we can't see that. that's why it's hard to understand.

[sanando]

I think you made a mistake near the end there? What you said didn't make sense, could you explain that please? You recalculated the XOR of the error induced output, then you realized that it still came 1 even with the error then without acknowledging that you said the error is there because the number of 1s is odd, but you also said that the receiver calculates the XORs again to check for errors, then why must the receiver calculate the XOR if all it needs to see is whether the 1s are odd or even? And if it does calculate it again, the answer comes out as 1 anyway, so how does it know it's an error? Something went wrong there as it doesn't make sense. Would be very kind of you if you could explain it in a comment or a video. Thank you.

[sunitadodiya]

Thank you sir for your hard work all your videos are good your whiteboard explanation is awesome. I really wanna request you to explain this topic on white board thank you s for reading 😊👏🤩👨‍🏫

[HassanRaza-nnro]

Buddy! I love your way of teaching. Best teacher ever.❤ I wish I could send you a gift.

[manishgupta]

Teach on white board with pen not like this

[saimajaved]

Thanks your lectures are very helpful . But I didn't understand this lec . Try to teach us on White board. Thanks

[waniyafarry]

sir, i think your first video that I couldn't understand this concept.

[anishkumargiri]

please do it slowly it's looking you are revising the concept