Given data:
D= 1001010101
G= 10011
The polynomial expression of G:
X4 + 0 x X3 + 0 x X2 + X + X0
= X4 + X + 1
Here, the degree of the expression is 4. So, r=4
Thus , D + r becomes 10010101010000
1 0 0 1 0 1
1 0 0 1 1
0 0 0 0 1 1
1 0
0 1
1
0 1 0 1 0 0 0 0
0
0
0
0
1
1
0
0
10011
100011000
0
1
1 1
1 1
0 0 0 0 0
0 0 0 0
There for, the value of R = 0000
So, the 7-bit generator, G= 10011 and D has the value 1001010101 then
the value of R is 0000