1.
What is the rate of the hamming code of parity bit m=8?
A
0.94
B
0.92
C
0.90
D
0.97
Answer and explanation
Correct Answer: D — 0.97
For m=8: total bits = 255, data bits = 247. Rate = 247/255 = 0.969 ≈ 0.97.
ObjectiveMcq
Print Protected
This page is protected for print. Use the website to view the content.
15 practice sets · Page 1 of 1
What is the rate of the hamming code of parity bit m=8?
0.94
0.92
0.90
0.97
For m=8: total bits = 255, data bits = 247. Rate = 247/255 = 0.969 ≈ 0.97.
For a hamming code of parity bit m=8, what is the total bits and data bits?
(255, 247)
(127, 119)
(31, 26)
(0, 8)
Total bits = 2^m - 1 = 2^8 - 1 = 255. Data bits = 2^m - m - 1 = 256 - 8 - 1 = 247. So the answer is (255, 247).
What is the code rate of a repetition Hamming code (3, 1)?
1
3
1/3
1.3
The code rate is the second number divided by the first number. For (3, 1), the rate = 1/3.
An Extended Hamming code is also called as:
SEDDEC
SEDDED
SECDED
SECDEC
An Extended Hamming code is called SECDED (Single Error Correction Double Error Detection). The most popular codes are (72, 64) and (127, 120).
________ is the mechanism of sending data bits multiple times to ensure consistency.
Repetition
Duplication
Mirroring
Redundancy
Repetition involves sending the same data bits multiple times. For example, with n=3 repetition, a bit '1' is sent as '111'. If the received bits differ, an error has occurred.
Including a parity bit along with the data surely detects all errors.
True
False
If an error occurs in the data string, parity changes to indicate it. However, if the error occurs in the parity bit itself, the error goes undetected.
A two-out-of-five code consists of:
Two 0s and three 1s
Three 0s and two 1s
Four 0s and one 1
One 0 and four 1s
A two-out-of-five code consists of three 0s and two 1s, giving ten possible combinations to represent digits 0–9.
What is the rate of hamming codes?
1 - r/(2^r - 1)
1 - r/2^r
1 + r/2^r
r/2^r + 1
Rate of a hamming code = message length / block length = (2^r - r - 1) / (2^r - 1) = 1 - r/(2^r - 1). It is the highest rate for a minimum distance of 3.
What is the message length 'k' of a Hamming(7, 4) code?
2^r - 1
2^r - r + 1
2^r - r - 1
2^(r+1) - r
For a Hamming(7, 4) code, the message length k = 2^r - r - 1, where r is the number of parity bits. Here r = 3, so k = 4.
What is the total block length 'n' of a Hamming code?
2^r
2^r - 1
2^(r-1) - 1
2^r + 1
For a Hamming(7, 4) code, the block length n = 2^r - 1, where r is the number of parity bits. Here r = 3, so n = 7.
Who invented Hamming codes?
Richard Hamming
Ross Hamming
Shannon
Huffman
Richard W. Hamming invented hamming codes at Bell Telephone Laboratory to minimize errors in punched card readers. Huffman invented Huffman codes. Shannon invented Shannon-Fano codes.
Hamming codes can be used for both single-bit error and burst error detection and correction.
True
False
Hamming codes are suitable only for single-bit error detection and correction, and two-bit error detection. They are very unlikely to detect burst errors.
Why do we require hamming codes?
Error correction
Encryption only
Decryption
Bit stuffing
Hamming codes are used for error detection and correction, channel encoding and decoding. They are linear-error correcting codes.
What is the minimal Hamming distance between any two correct codewords?
1
2
3
4
Since we use a generalized version of Hamming(7, 4) code, the minimal hamming distance is 3. It cannot correct burst errors.
The most common hamming codes are a generalized version of?
Hamming(7, 4) code
Hamming(8, 4) code
Hamming(6, 3) code
Hamming(5, 7) code
The most common hamming codes generalize to form Hamming(7, 4) code. It encodes four bits of data into seven bits by adding three parity bits.