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?

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
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**Error-Correcting Code for Memory Words of Length 10**

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?**

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**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 represent 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?)
Transcribed Image Text:**Error-Correcting Code for Memory Words of Length 10** 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 represent 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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