Question

Given a 8-bit word 00111001, suppose when the word is read from memory, the new check bits are calculated based on the fetched reading is 0001. Provide details regarding how you get the answer.

Part 1) Is the data fetched correctly?
Part 2) If no, is the data bit or check bit goes wrong?
Part 3) What is the additional checking bit that you need to store in the memory if you want to use it to detect two bits error?

Answer 1

Part 1).

Calculating hamming code check bits for the data

The check bit positions will be 2⁰ = 1, 2¹ = 2, ,2² = 4 , and 2³ = 8

12	11	10	9	8	7	6	5	4	3	2	1
0	0	1	1	C8	1	0	0	C4	1	C2	C1
				0			0	1		1	1

Considering even parity

The check bits are in bit numbers 8, 4, 2, and 1.

Check bit for c8 = D12 ® D11® D10 ® D9 =0®0®1®1=0

Check bit for c4= D12® D7® D6® D5 =0®1®0®0=1

Check bit for c2 =D11® D10® D7® D6 ® D3 =0®1®1®0®1=1

Check bit for c1 =D11® D9® D7® D5 ® D3 =0®1®1®0®1=1

Thus, the check bits are: 0 111

This does not matches with the calculated check bit 0001.So there is an error.The data has not fetched correctly.

2) for the wrong bit we xor(0111, 0001) = 0110 =6

So there is an error in the 6^th bit. Which is a data bit.

3.An extended Hamming code having one extra parity bit is often used. Extended Hamming codes achieve a Hamming distance of four, which allows to check when any two-bit errors occur.