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

Explanation / Answer

1)

1111 1010 = FA
1100 0111 = C7
1100 0110 = CE
0001 0001 = 11
1011 1011 = BB
0110 0101 = 65
1010 1101 = AD
1100 0001 = C1

3 rd ROW :
1100 1110 -> odd numbe of 1 bits but parity bit is 0

4th COLUMN :
1
0
0
1
1
0
1
0
--
1 which is wrong
--

Row number 3
row and column are reflecting are wrong bit as per the column partity bit

1100 1110 -> odd numbe of 1 bits but parity bit is 0

recieved : FA C7 CE 11 BB 65 AD C1
corrected actual : FA C7 C6 11 BB 65 AD C1

2)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.