Answer:
1. ∑ numbers=57
Overall ∑ is 57 hence.
And each number is less than 15, and hence they can be represented in 4 bits
However, we cannot write 57 in 4 bits.
However, 111001 is 57 in binary, and it is as well greater than 4 bits.
Hence, we are adding the two extreme left bits to right 4 bits as mentioned below.
Left are 11, right bits are 1001
1001
11
1110 is the checksum
=14 and this is 14 bits.
2. The degree of given polynomial is 3, and hence,
The divisor is X3+1 =1001
Original data word=10110
Since the size of CRC is 3 bits, we should place 3 zeros to the right of the original data
And thus we get,
10110000
10100
1001√10110000
1001
00100000
1001
--------------
0100 CRC
We send our data 10110 its reminder (CRC) will be added with it like 10110100
Receiver will receive 10110100 with same divisor 1001
10100
1001√10110100
1001
---------------------------
01001
1001
--------------------------------
000
And since the last 3 bits are zero, and hence its error free.
3.
At 7 and 5 we have 1 and similarly in 2nd at 8, 4 and 0
Bits Polynomial
1010000 X7+X5+0
10001001 X8+X4+1
Explanation:
Please check answer.
