Answered: 5. Suppose we want an error-correcting…

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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5. Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10.

a. How many parity bits are necessary?

b. Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code and an odd parity, find the code word to present the 10-bit information word:

\[1 \, \underline{0} \, 0 \, 1 \, 1 \, 0 \, 0 \, 1 \, 1\]

c. We now receive the following code word:

\[1 \, \underline{0} \, 1 \, 0 \, 1 \, 1 \, 0 \, 0 \, 0 \, 1 \, 0 \, 1 \, 1\]

Is this a legal code word, assuming an odd parity? If not, what is the corrected code word? (Which bit is the error bit?)

Expert Solution

Step 1

Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10.

a. How many parity bits are necessary?

b. Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code and an odd parity, find the code word to present the 10-bit information word:

1 0 0 1 1 0 0 1 1 1

C. We now receive the following code word:

1 0 1 0 1 1 0 0 0 0 1 0 1 1

Is this a legal code word, assuming an odd parity? If not, what is the corrected code word? (Which bit is the error bit?)

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