The sender keeps the long-division remainder. This lesson shows how that remainder becomes the bits appended to the message.
highlighted = computed this step
Why the remainder is transmitted
The sender does not transmit the quotient. It transmits the original message followed by the recomputed remainder.
CRC=100
Remainder becomes CRC
The remainder 100 is the CRC. Appending it to the message gives codeword 11010011101100100.
11010011101100∥100=11010011101100100
Decode it again
For message 10011010, the same generator gives CRC 001 and codeword 10011010001.
10011010+001=10011010001
Summary
The CRC is the final remainder, and the codeword is message plus remainder. Polynomial arithmetic over the exact bits; timing/throughput is not modeled here.