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Odd parity Hamming code for 1011
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## Odd Parity Hamming code

• 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 Hamming (7, 4) code, 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.
• 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