A 16 number ID was sent over the Internet in the form of eight, 8-bit words; a n

Question

A 16 number ID was sent over the Internet in the form of eight, 8-bit words; a ninth last bit on the right indicates the parity or the number of 1 bits; even = 0, odd = 1 in the original 8-bit word. So we might send the following 16 number ID: 3A98 6B11 FE59 CD72. The first 2 numbers 3A would be sent as the following 9-bits (an 8-bit word, plus a parity bit): 0011 1010 0 (3 A with parity bit 0). In error correcting code, for every 8 words an additional 9th word is sent, call it the parity word. If you presented the original 8 words (including the parity bit column) as a 9 x 9 matrix, each bit in the parity word would be the parity bit for each column. (For the mathematically inclined you can prove that the parity bit calculated for the parity word (9th row) is identical to the parity bit calculated for the 9th column, using mod 2 arithmetic).

2. Duplicate Error Correction Code Problem

3. Triplicate Error Correction Code Problem

This is the problem. A 16 number ID was sent in error correcting code format as nine, 9-bit strings. Here are the 81 bits that were received, which have been arranged for you visually as a 9 x 9 matrix. The basic assumption that due to noise or whatever at most 1 bit in the 81 bits could have been switched from a 0 to a 1 or from a 1 to a 0. The following 81 bits were received. Parity Bit Converted to 2 Numbers 0 F 110001111 11001 1100 00010 0 01(0 101110110 0110 0101(0 101011011 110000011 010110001 Parity Row The 16 number ID that was received is: The 16 number ID that was originally sent was:

Explanation / Answer

1.

The parity number obtained is:

001110100

The parity number Originally sent was 1:

110100111

2.10000 and 01100

3.10011 and 11001

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