Jan 21&29(HD) Flashcards
What is the Hamming Distance of real-life Hamming code? Explain how you know. Also, how many errors can be detected and corrected by Hamming code?
The Hamming distande of real-life Hamming code is 3 bits. This is because each bit change in the dataword will change at least 3 bits in the codeword. 1 for the data bit, and 2 for the lowest number of parity bits checking the data bit. Hamming code can detect errors of up to 2 bits, and correct errors of up to 1 bit.
If the Hamming distance of a code is R bits, how many bit errors can it detect and correct? Why not more than those amounts?
It can detect R-1(inclusive) because an error in R bits will result in a valid codeword which can’t be detected. For correction, it can fix errors in up to (R-1)/2 bits. If there are more errors than this, the system might mistakenly ‘correct’ the data to the wrong sequence, which is not the original intended data.
Define Hamming distance.
The minimum number of bits different between any 2 valid words in a code.
codeA:
only 00000000 and 11111111 are valid.
codeB: 00000000 and 11111111 are invalid.
?Which one is better for detecting and correcting errors and why?
Code A is better for finding and fixing small errors compared to Code B. It works well when there are minor changes. For example, if the original code is 00000000 and it changes a little, like to 00100000 or 01001000, Code A can correct these errors. However, it’s not as effective with bigger errors. It can’t fix situations where 00000000 changes to something very different, like 00001111 or 11111110. In short, Code A is good for small errors but not for large or complex ones.
Why must numbers be stored in the same direction across different system, but letters in strings don’t require the same consistency?
Numbers require consistent byte ordering because their value is dependent on the sequence of bytes(e.g. an integer is typically 4 bytes). A change in byte order can alter the numerical value. In contrast, each character in a string is independent and typically 1 byte, and its meaning is not affected by byte order.
Do we want a small or large Hamming distance? Why?
Larger Hamming distance. Because Hamming Distance refers to The minimum number of bits different between any 2 valid words in a code, so that indicates a greater difference between valid words, resulting in an increased capacity to detect and correct errors.
If a code has a Hamming distance of 14 bits, how many errors can it detect? Why not more than that?
13 errors are detectable because 14 errors are actually a valid word.
Which data bits are checked by bit4 in a 21-bit codeword? Explain how you know.
But 5,6,7,12,13,14,15,20, and 21 because they can be broken down into power of 2 that include 2^2=4
