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Hamming codes are the most efficient single-bit-error correcting codes. For a Hamming code with e check bits, bits in the code word are numbered from 1 to 2c -1 and the check bits occupy the power of 2 positions, i.e. positions 1, 2, 4, 8, .. The remaining positions are filled by the data bits. The ith check bit is a parity over all bits where the bit position in binary has a 1' in the ith bit. So, the first check bit is a parity over positions 1, 3, 5, 7, ... the second check bit is a parity over positions 2, 3, 6, 7,.., etce. For e = 3, a Hamming code word has the form cle2dlc3d2d3d4 (with bit numbering from left to right). For example, the Hamming code word for data 0110 is 1100110 (using even parity). 4) Compute the 4-bit data words corresponding to the following 7-bit words, which could be valid Hamming code words or could have single-bit errors inserted. Even parity is used in all cases. Show your work. (a) 0011000 (b) 1011101

Hamming codes are the most efficient single-bit-error correcting codes. For a Hamming code with e check bits, bits in the code word are numbered from 1 to 2c -1 and the check bits occupy the power of 2 positions, i.e. positions 1, 2, 4, 8, .. The remaining positions are filled by the data bits. The ith check bit is a parity over all bits where the bit position in binary has a 1' in the ith bit. So, the first check bit is a parity over positions 1, 3, 5, 7, ... the second check bit is a parity over positions 2, 3, 6, 7,.., etce. For e = 3, a Hamming code word has the form cle2dlc3d2d3d4 (with bit numbering from left to right). For example, the Hamming code word for data 0110 is 1100110 (using even parity). 4) Compute the 4-bit data words corresponding to the following 7-bit words, which could be valid Hamming code words or could have single-bit errors inserted. Even parity is used in all cases. Show your work. (a) 0011000 (b) 1011101

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Hamming codes are the most efficient single-bit-error correcting codes. For a Hamming code with c check bits, bits in the code word are numbered from 1 to 2c -I and the check bits occupy the power of 2 positions, i.e. positions 1, 2, 4, 8, .. The remaining positions are filled by the data bits. The ith check bit is a parity over all bits where the bit position in binary has a ʻ1’ in the ith bit. So, the first check bit is a parity over positions 1, 3, 5, 7, .., the second check bit is a parity over positions 2, 3, 6, 7,.., etc. For e = 3, a Hamming code word has the form clc2dlc3d2d3d4 (with bit numbering from left to right). For example, the Hamming code word for data 0110 is 1100110 (using even parity). 4) · Compute the 4-bit data words corresponding to the following 7-bit words, which could be valid Hamming code words or could have single-bit errors inserted. Even parity is used in all cases. Show your work. (a) 0011000 (b) 1011101
Transcribed Image Text:Hamming codes are the most efficient single-bit-error correcting codes. For a Hamming code with c check bits, bits in the code word are numbered from 1 to 2c -I and the check bits occupy the power of 2 positions, i.e. positions 1, 2, 4, 8, .. The remaining positions are filled by the data bits. The ith check bit is a parity over all bits where the bit position in binary has a ʻ1’ in the ith bit. So, the first check bit is a parity over positions 1, 3, 5, 7, .., the second check bit is a parity over positions 2, 3, 6, 7,.., etc. For e = 3, a Hamming code word has the form clc2dlc3d2d3d4 (with bit numbering from left to right). For example, the Hamming code word for data 0110 is 1100110 (using even parity). 4) · Compute the 4-bit data words corresponding to the following 7-bit words, which could be valid Hamming code words or could have single-bit errors inserted. Even parity is used in all cases. Show your work. (a) 0011000 (b) 1011101
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