computer networks 18 hamming code cs it gate crash course

Download 1M+ code from https://codegive.com/2b45db6 computer networks: hamming code tutorial *overview of hamming code:* hamming code is an error-detecting and error-correcting code that was developed by richard hamming. it is widely used in computer networks and data transmission systems to ensure data integrity. hamming codes are capable of detecting up to two-bit errors and correcting one-bit errors. key concepts of hamming code 1. **data bits and parity bits**: data bits (k): the actual data bits you want to send. parity bits (r): extra bits added to the data to help detect and correct errors. 2. **calculating the number of parity bits**: the number of parity bits required can be calculated using the formula: \[ 2^r \geq k + r + 1 \] where \( r \) is the number of parity bits and \( k \) is the number of data bits. 3. **positioning of parity bits**: parity bits are placed in positions that are powers of two (1, 2, 4, 8, ...). the other positions are filled with data bits. 4. **calculating parity bits**: each parity bit checks specific bits in the codeword. the parity check ensures that the total number of 1s in the checked bits (including the parity bit) is even. hamming code implementation let's go through a simple example of encoding and decoding using hamming code. example: encoding with hamming code 1. **select data bits**: let's say we have 4 data bits: `1011`. 2. **calculate number of parity bits**: for 4 data bits (k = 4): we need to find \( r \) such that \( 2^r \geq 4 + r + 1 \). trying \( r = 3 \): \( 2^3 = 8 \) which satisfies the condition. 3. **create the hamming code structure**: the bit positions will be as follows: position 1: p1 (parity) position 2: p2 (parity) position 3: d1 (data bit) position 4: p4 (parity) position 5: d2 (data bit) position 6: d3 (data bit) position 7: d4 (data bit) so the initial setup looks like: ``` p1 p2 d1 p4 d2 d3 d4 ``` 4. **fill in data bits**: plac ... #ComputerNetworks #HammingCode #windows Computer networks Hamming code CS IT GATE crash course error detection data transmission coding theory network reliability digital communication information theory error correction network security algorithm design