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Consider the 5-bit generator, g=10011, and suppose that d has the value

A) 11010
B) 10101
C) 01100
D) 11111

1 Answer

5 votes

Final answer:

Performing modulo-2 division, we find that none of the given data values are divisible by the generator polynomial 10011.

Step-by-step explanation:

To determine whether a given data value is divisible by a generator polynomial, we perform a modulo-2 division operation. In this case, the generator polynomial is represented by 10011 which has a degree of 4. We can perform the modulo-2 division by dividing the given data value by the generator polynomial using binary long division.

A) For d = 11010:

10011
11010 | 100010
-10011
_____
1000
1001
____
110
1001
___
111
1001
___
10

The remainder is 10, which means the given data value is not divisible by the generator polynomial.

B) For d = 10101:

10011
10101 | 100000
-10011
_____
10001
10011
_____
101
10011
____
10

The remainder is 10, which means the given data value is not divisible by the generator polynomial.

C) For d = 01100:

10011
01100 | 001001
-00000
_____
10011
10011
_____
10100
10011
_____
1101
10011
_____
1100

The remainder is 1100, which means the given data value is not divisible by the generator polynomial.

D) For d = 11111:

10011
11111 | 1001010
-10011
__________
11010
10011
______
1001
10011
_____
1011
10011
_____
1100

The remainder is 1100, which means the given data value is not divisible by the generator polynomial.

User CPB
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