Answer:
1.. Total number of 6 bit strings is 64
2. Number of 6-bit strings with weight of 0 is 1
3. Number of 6-bit strings with weight of 1 is 6
4. Number of 6-bit strings with weight of 3 is 20
5. Number of 6-bit strings with weight of 5 is 6
6. Number of 6-bit strings with weight of 6 is 1
7. Number of 6-bit strings with weight of 7 is 0
Step-by-step explanation:
A bit string is a string that contains 0 and 1 only
1. Total number of 6 bit strings is 2^6 = 64
2. Number of 6 bit strings with weight 0 is 1
Explanation
Weight 0 means a string with no occurrence of 1
Here, we are only interested in occurrence and not order of occurrence
We apply combination formula for this
nCr = n!/(n-r)!r!
n = 6 and r = 0 i.e. no occurrence of 1
6C0 = 6!/(6-0)!0!
6C0 = 6!/6!0!
6C0 = 1
Hence, the number of string with weight 0 (i.e. no occurrence of 1 ) is 1
3. Number of string with weight 1 is 6
Explanation
Weight 0 means a string with exactly 1 occurrence of '1'
Here, we are only interested in occurrence and not order of occurrence
We apply combination formula for this
nCr = n!/(n-r)!r!
n = 6 and r = 1
6C1 = 6!/(6-1)!1!
6C1 = 6!/5!1!
6C1 = 6
Hence, the number of string with weight 6
4. Number of string with weight 3 is 20
Explanation
n = 6 and r = 3
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
6C3 = 20
Hence, the number of string with weight 3 is 20
5. Number of string with weight 5 is 6
Explanation
n = 6 and r = 5
6C5 = 6!/(6-5)!5!
6C5 = 6!/1!5!
6C5 = 6
Hence, the number of string with weight 5 is 6
6. Number of string with weight 6 is 1
Explanation
n = 6 and r = 6
6C6 = 6!/(6-6)!6!
6C6 = 6!/0!6!
6C6 = 1
Hence, the number of string with weight 6 is 1
7. Number of string with weight 7 is 0
Weight of 7 means that a string that has 7 occurrence of 1
The total length of a 6 bit is 6
Since 6 is less than 7, there's no way a bit of weight 7 can occur.
So, the right answer for this is 0.
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