Designing a Hamming SECEDED System - Need Help!

[Petkovsky]

Ok, so, i need to design a system with a sender and a receiver. There are 4 bits to be sent which need to be encoded using Hamming SECEDED code. Now, i need to design all the hardware individually, meaning that the receiver, the channel and the sender need to be broken down and using simple Boolean functions i need to draw a scheme for the individual parts. I managed to do everything except the error correcting part.

I can calculate the syndrome, and I know which bit was sent incorrectly, however i don't know how to build a circuit using AND, OR EXOR and NOT functions which will find the wrong bit and fix it. I guess i should have 7 inputs, one for each bit, but can't seem to understand how to use the syndrome to correct the sent data.

Anyone?

 

[Valkarie]

The error-correcting circuit should be based on the parity check matrix associated with the Hamming code. This matrix is used to calculate the syndrome of the received code, which can tell us which bit is wrong. The circuit should then use this information to identify which bit needs to be flipped, and apply the necessary logic to do so. For example, assume we are using a 4-bit Hamming code. The corresponding parity check matrix is:1 1 0 1 1 0 1 0 0 1 1 0 To calculate the syndrome, take the received 4-bit code, and multiply it by this matrix. If the result is all zeros, then the code was received correctly; if not, then we can tell which bit is wrong. Once we know which bit is wrong, we can apply the necessary logic to correct it. For example, if bit 2 is incorrect, the circuit could be designed to have a NOT gate following bit 2, which would flip its value (i.e. from 0 to 1, or from 1 to 0). In summary, the error-correcting circuit should be designed around the parity check matrix for the Hamming code. This matrix is used to calculate the syndrome, which tells us which bit is wrong, and the logic can then be applied to correct it.

 

[piercas]

I would suggest breaking down the problem into smaller parts and approaching it systematically. First, make sure you have a solid understanding of the Hamming SECEDED code and how it works. This will help you understand the purpose and function of each individual hardware component in the system.

Next, focus on the error correction part. You mentioned that you can calculate the syndrome and identify which bit was sent incorrectly. This is a good start. Now, you can use Boolean functions to create a circuit that will take the syndrome and use it to correct the error. This circuit will need to have 7 inputs, one for each bit, as you mentioned. You can use AND, OR, EXOR, and NOT functions to manipulate the bits and fix the error.

To better understand how to use the syndrome to correct the error, you can refer to the Hamming SECEDED code algorithm. This will help you understand the logic behind the error correction process and guide you in designing the circuit.

Additionally, you can also look for examples or tutorials online that demonstrate how to design a Hamming SECEDED system and correct errors using Boolean functions. This may provide you with a visual aid and help you better understand the concept.

Overall, designing a Hamming SECEDED system with error correction can be challenging, but with a systematic approach and a solid understanding of the code, you should be able to successfully design the circuit. Don't hesitate to seek help from other experts in the field or online resources if needed.