5. Hamming Codes a) Suppose we want an error correcting code that will allow all single-bit errors to be corrected for memory words of length 15. How many check bits are necessary? b) Suppose we are now working with memory words of length 8. We have already calculated that we need 4 check bits, and the length of all codewords will be 12. We now receive the following code word: 010011011111 Is this a legal codeword, assuming even parity? If not, where is the error?

5. Hamming Codes a) Suppose we want an error correcting code that will allow all single-bit errors to be corrected for memory words of length 15. How many check bits are necessary? b) Suppose we are now working with memory words of length 8. We have already calculated that we need 4 check bits, and the length of all codewords will be 12. We now receive the following code word: 010011011111 Is this a legal codeword, assuming even parity? If not, where is the error?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

5. Hamming Codes
a) Suppose we want an error correcting code that will allow all single-bit errors to be
corrected for memory words of length 15. How many check bits are necessary?
b) Suppose we are now working with memory words of length 8. We have already
calculated that we need 4 check bits, and the length of all codewords will be 12. We
now receive the following code word:
010011011111
Is this a legal codeword, assuming even parity? If not, where is the error?

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