(ii) 11001001011

The generator polynomial x^3 + 1 corresponds to the bit pattern 1001 (degree 3 → 4-bit divisor, coefficients of x^3,x^2,x^1,x^0 = 1,0,0,1). The number of CRC bits to append = degree of generator = 3 bits.

Step 1: Append 3 zero bits to the message: 11001001 → 11001001000

Step 2: Divide this by the generator 1001 using XOR (mod-2 division), tracking the remainder:

11001001000  ÷  1001  (mod-2 division)

1100  XOR 1001 = 0101
bring down 1 → 1011  XOR 1001 = 0010
bring down 0 → 0100  (leading 0, no XOR)
bring down 0 → 1000  XOR 1001 = 0001
bring down 1 → 0011  (leading 0, no XOR)
bring down 0 → 0110  (leading 0, no XOR)
bring down 0 → 1100  XOR 1001 = 0101
bring down 0 → 1010  XOR 1001 = 0011

Remainder (last 3 bits) = 011

Step 3: Replace the appended zeros with this remainder:

Transmitted message = 11001001 + 011 = 11001001011

This matches option (ii).