Answer these following question very urgent "file attch"

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

10001001X8+X4+1

Explanation:

Please check answer.