Digital-Systems-HW2
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Arizona State University *
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Electrical Engineering
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Feb 20, 2024
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Uploaded by EarlCrown13337
Digital Systems HW#3
1.
Write the following message in code ascii + parity bit: "good luck!!"
011001111, 011011110, 011011110, 011001001, 001000001, 011011000,
011101011, 011000110, 011010111, 001000010, 001000010
2.
Given a 10-bit code word representing 600 different characters, how many
errors can be detected and how many corrected?
None. The distance must be 1.
3.
Given the following code words:
011011011011
101101101101
110110110110
a.
Determine the distance between them.
8
b.
Find a new word with distance 4 from the code.
111111111111
c.
Find a new word with distance 8 from the code.
000000000000
d.
How many errors can be detected in the original code? How many
errors can be corrected?
8=2*c+d+1, correct=c, detect=c+d
correct=0, detect=7
correct=1, detect=6
correct=2, detect=5
correct=3, detect=4
4.
The following message was received in code Hamming over a very noisy
channel, with each word corrupted with one error. Decrypt the original
message: 1101000 0010001 1110110 0011011
1101001 0011001 1100110 0011001
5.
General literacy in Chinese requires about 3000 characters. What is the
minimal number of bits required to represent them in code Hamming
(allowing for 1-bit error correction)?
3000 <= 2^m
m >= log
2
(3000)
log
2
(3000) = 11.55
m = 12
2^k > m + k
k = 5
Total bits = m + k = 17
6.
Two numbers are given and represented in two-dimensional code. In this
code, the rightmost column holds the parity bit for each row, while the bottom
row holds the parity bit for each column. For each number, determine if there
are any errors. If possible, make the appropriate corrections. If not, explain
why it can't be corrected.
The first code has at least 3 errors and cannot be corrected
because we don’t know which incorrect horizontal parity bit
matches which incorrect vertical parity bit.
The second code has at least 1 error which is the rightmost middle
bit is supposed to be a 1.
7.
Given the following words:
011011011011, 101101101101, 110110110110
a.
Convert them from binary to Gray.
010110110110, 111011011011, 101101101101
b.
Convert the words from Gray to binary.
010010010010, 110110110110, 100100100100
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