The carry bit together with the 16 bit register gives 17 bits.When sending data, short checksum is generated based on data content and sent along with data.
When receiving data, checksum is generated again and compared with sent checksum. Javascript CRC-16 Calculator Here is a Javascript CRC-16 calculator I have written to demonstrate the different techniques that can be used to implement the CRC calculation in code. Hex File Crc 16 Calculator Online Generator Polynomial IntoA CRC is calculated by dividing a generator polynomial into the message. The long division process is done according to the mathemetics of polynomial division mod 2, so the conventional long division process is not used. Instead the various left shifts of the generator polynomial bit pattern are simply XORed into the message bit pattern. Since the msb is always 1, when the polynomial is written in hex form it is the convention just to show the lower 16 bits. For example the IBM polynomial 18005 is usually just written as 8005. Long Division Method To visualise the long division process, imagine the message written as a binary number (or bit pattern). The leading bits in the message will be the most significant (or leftmost) bits in the bit pattern. The long division process is begun by left shifting the 17 bit polynomial such that the msb of the polynomial is aligned with the msb of the message. The polynomial is XORed into the message only if the msb of the message is 1 and as a result the msb of the message will be cleared. The polynomial is then right shifted by 1 bit and the process repeats. In this way every bit in the message is tested against the polynomial, with the polynomial being XORed into the message if the message bit that is aligned with the msb of the shifted polynomial is 1. Of course the bits in the message will change as the polynomial is XORed into it, and all of the bits to the left of the current shifted polynomial will become 0. To capture the remainder, 16 zero bits are appended to the right of the message bit pattern. When the long division process reaches the point where the msb of the polynomial is aligned with the lsb (the rightmost bit) of the message and the final XOR is done (only if the lsb was 1) these 16 bits will hold the CRC value. Register Method If the CRC is being computed on a machine where there is a lot of memory and processing power available, then it is easy to implement the above long division method. Then shift and XOR the polynomial array into the message array as described above. However on an embedded system where the memory and processing power is limited, this approach is not feasible. Even though the polynomial for 16 bit CRC is 17 bits in length, a CRC-16 calculation can be done with a 16 bit register. One, when an operation is performed on a register that results in a carry from the msb of the data contained in the register, the CPU will capture and store the carry bit. ![]() Three, all bits in the message that are to the left of the shifted polynomial are cleared and will not be a part of the final CRC value.
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