Consider the 5-bit generator, G = 10011, and suppose that D has the value1010101010. What is the value of R?

To calculate the value of R, we need to perform polynomial long division of D by G. Here are the steps:

1. Append four 0s to the end of D to create a dividend with 14 bits: 10101010100000.
2. The first 5 bits of the dividend are divided by G=10011 to get the first bit of the quotient and the remainder. The first bit of the quotient is 1 and the remainder is 1110.
3. The next bit of the dividend (which is a 0) is brought down to the remainder to create a new 5-bit sequence: 11100.
4. This new sequence is divided by G to get the next bit of the quotient and remainder. The next bit of the quotient is 0 and the remainder is 1010.
5. Steps 3 and 4 are repeated until we have a quotient of 10 bits.
6. The final remainder is R. In this case, R=1010.

Therefore, the value of R is 1010.