7-bits even parity Hamming code is received as 1100010

In 7-bits Hamming code 4-bits (D3, D5, D6 & D7) represents data bits and 3-bits (P1, P2, & P4) are parity bits.

This 7-bit Hamming code is represented as follows:

To check whether the received Hamming code is correct or not let's perform the following operations:

Take the bits present at the below-mentioned places

Parity bit-1 covers all the bits positioned at bit-position 1, 3, 5, 7, 9, 11,.. etc.

Therefore,

C1 = Even_Parity(1, 3, 5, 7) = 1 0 0 0 = 1 (Odd number of 1,s, which means error is present)

Parity bit-2 covers all the bits positioned at 2, 3, 6, 7, 10, 11,... etc.

Therefore,

C2 = Even_Parity(2, 3, 6, 7) = 1 0 1 0 = 0 (Even number of 1's, which means No error is present)

Parity bit-4 covers all the bits positioned at 4–7, 12–15, 20–23,... etc.

Therefore,

C4 = Even_Parity(4, 5, 6, 7) = 0 0 1 0 = 1 (Odd number of 1's, which means error is present)

Therefore,

C = C4 C2 C1 = 1 0 1 = It represent decimal number 5

That means a Single bit error is present at the $5^{th}$ position of received Hamming code 1100010.

Now, remove the $5^{th}$ position single bit error.

The $5^{th}$ bit holds 0 which creates an error in a Hamming encoded 7-bit number. Hence, to remove this error 0 is replaced with 1.

Therefore,

The Corrected Error Free 7-bits Hamming Code is 1100110