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Odd parity Hamming code for 1011

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Odd parity Hamming code for 1011

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written 4 months ago by |

- The given number is
**1011**which holds 3 bits of 1's. Therefore, it represents the*Odd Parity.* - The given number is 4-bits code hence, there are 3 parity bits p1, p2, and p3.
- This is also called
, which is a linear error-correction methodology that encodes 4-bits of data into 7-bits, by addition of 3 (P1, P2, P3) parity bits.*Hamming (7, 4) code* - Therefore, the resultant 7-bits hamming code looks as follows:

Bit Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Resultant Hamming Number |
P1 |
P2 |
d1 | P3 |
d2 | d3 | d4 |

Here, d1, d2, d3, and d4 represent the 4-bits of code 1011.

Therefore,

*d1 = 1, d2 = 0, d3 = 1, and d4 = 1*

The value of P1, P2, and P3 calculated as follows:

$P1 = d1 \oplus d2 \oplus d4$

$P2 = d1 \oplus d4 \oplus d3$

$P3 = d2 \oplus d4 \oplus d3$

Therefore,

$P1 = d1 \oplus d2 \oplus d4 = 1 \oplus 0 \oplus 1 =0$

$P2 = d1 \oplus d4 \oplus d3 = 1 \oplus 1 \oplus 1 = 1$

$P3 = d2 \oplus d4 \oplus d3 = 0 \oplus 1 \oplus 1 = 0$

Now, the final Resultant Hamming Code looks as follows:

P1 | P2 | d1 | P3 | d2 | d3 | d4 |
---|---|---|---|---|---|---|

0 | 1 | 1 | 0 | 0 | 1 | 1 |

Odd parity Hamming code for 1011 is *0110011*

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