4.d. Cyclic Redundancy Check (CRC) Error Detection

For certain applications, verifying the integrity of the data you are sending and receiving can be very important. Because of this, the jrk has optional 7-bit cyclic redundancy checking, which is similar to a checksum but more robust as it can detect errors that would not affect a checksum, such as an extra zero byte or bytes out of order.

Cyclic redundancy checking can be enabled by checking the “Enable CRC” checkbox in the configuration utility. In CRC mode, the jrk expects an extra byte to be added onto the end of every command packet. The most-significant bit of this byte must be cleared, and the seven least-significant bits must be the 7-bit CRC for that packet. If this CRC byte is incorrect, the jrk will generate its Serial CRC error and ignore the command. The jrk does not append a CRC byte to the data it transmits in response to serial commands.

A detailed account of how cyclic redundancy checking works is beyond the scope of this document, but you can find a wealth of information using Wikipedia. The CRC computation is basically a carryless long division of a CRC “polynomial”, 0x91, into your message (expressed as a continuous stream of bits), where all you care about is the remainder. The jrk uses CRC-7, which means it uses an 8-bit polynomial and, as a result, produces a 7-bit remainder. This remainder is the lower 7 bits of the CRC byte you tack onto the end of your command packets.

The CRC implemented on the jrk is the same as the one on the qik motor controller but differs from that on the TReX motor controller. Instead of being done MSB first, the computation is performed LSB first to match the order in which the bits are transmitted over the serial line. In standard binary notation, the number 0x91 is written as 10010001. However, the bits are transmitted in this order: 1, 0, 0, 0, 1, 0, 0, 1, so we will write it as 10001001 to carry out the computation below.

The CRC-7 algorithm is as follows:

1. Express your 8-bit CRC-7 polynomial and message in binary, LSB first. The polynomial 0x91 is written as 10001001.
2. Add 7 zeros to the end of your message.
3. Write your CRC-7 polynomial underneath the message so that the LSB of your polynomial is directly below the LSB of your message.
4. If the LSB of your CRC-7 is aligned under a 1, XOR the CRC-7 with the message to get a new message; if the LSB of your CRC-7 is aligned under a 0, do nothing.
5. Shift your CRC-7 right one bit. If all 8 bits of your CRC-7 polynomial still line up underneath message bits, go back to step 4.
6. What’s left of your message is now your CRC-7 result (transmit these seven bits as your CRC byte when talking to the jrk with CRC enabled).

If you have never encountered CRCs before, this probably sounds a lot more complicated than it really is. The following example shows that the CRC-7 calculation is not that difficult. For the example, we will use a two-byte sequence: 0x83, 0x01.

Steps 1 & 2 (write as binary, add 7 zeros to the end of the message):

    CRC-7 Polynomial = [1 0 0 0 1 0 0 1]
    message = [1 1 0 0 0 0 0 1] [1 0 0 0 0 0 0 0] 0 0 0 0 0 0 0

Steps 3, 4, & 5:
                    _______________________________________________
    1 0 0 0 1 0 0 1 ) 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                  XOR 1 0 0 0 1 0 0 1 | | | | | | | | | | | | | | |
                      --------------- | | | | | | | | | | | | | | |
                        1 0 0 1 0 0 0 1 | | | | | | | | | | | | | |
           shift  ----> 1 0 0 0 1 0 0 1 | | | | | | | | | | | | | |
                        _______________ | | | | | | | | | | | | | |
                              1 1 0 0 0 0 0 0 | | | | | | | | | | |
                              1 0 0 0 1 0 0 1 | | | | | | | | | | |
                              _______________ | | | | | | | | | | |
                                1 0 0 1 0 0 1 0 | | | | | | | | | |
                                1 0 0 0 1 0 0 1 | | | | | | | | | |
                                _______________ | | | | | | | | | |
                                      1 1 0 1 1 0 0 0 | | | | | | |
                                      1 0 0 0 1 0 0 1 | | | | | | |
                                      _______________ | | | | | | |
                                        1 0 1 0 0 0 1 0 | | | | | |
                                        1 0 0 0 1 0 0 1 | | | | | |
                                        _______________ | | | | | |
                                            1 0 1 0 1 1 0 0 | | | |
                                            1 0 0 0 1 0 0 1 | | | |
                                            _______________ | | | |
                                                1 0 0 1 0 1 0 0 | |
                                                1 0 0 0 1 0 0 1 | |
                                                _______________ | |
                                                      1 1 1 0 1 0 0 = 0x17

So the full command packet we would send with CRC enabled is: 0x83, 0x01, 0x17.