Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8 d7 d6 d5 c8 d4

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Digital Logic paper.

Q: How can I prepare for GATE-CS Digital Logic?

To prepare for GATE-CS Digital Logic, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2021 question covers Computer Arithmetic topic.

Q: What is the difficulty level of this question?

This GATE-CS 2021 Digital Logic question has a hard difficulty level and is marked as an important question.

Q: Where can I find more GATE-CS previous year questions?

You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8 d7 d6 d5 c8 d4 d3 d2 c4 d1 c2 c1, where x and y are unknown data bits. The check bits are computed for even parity. Which one of the following choices gives the correct values of x and y?

Accepted Answer

Correct Answer: (A) x is 0 and y is 0Concept -- Hamming Code Parity Computation: In a (12,8) Hamming code with even parity, check bits are at positions 1, 2, 4, 8 (1-indexed). Each check bit provides even parity over a specific set of bit positions determined by whether the position number has a 1 in the corresponding bit of its binary representation.Given known bit values from the problem table, the unknown bits x (in d5) and y (in d8) are determined by the parity equations. Substituting known values into the parity equations for c8 (covering positions 8-12) and c4 (covering positions 4-5, 6-7, 12) and enforcing even parity for each check bit, solving the system yields x = 0 and y = 0.

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8 d7 d6 d5 c8 d4 d3 d2 c4 d1 c2 c1, where x and y are unknown data bits. The check bits are computed for even parity. Which one of the following choices gives the correct values of x and y?

Master GATE-CS with Our Test Series

More Questions from Computer Arithmetic

Frequently Asked Questions

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d8 d7 d6 d5 c8 d4 d3 d2 c4 d1 c2 c1, where x and y are unknown data bits. The check bits are computed for even parity. Which one of the following choices gives the correct values of x and y?

Master GATE-CS with Our Test Series

More Questions from Computer Arithmetic

Frequently Asked Questions