6. Cyclic Redundancy Check (CRC) Error Detection

6.a. CRC Computation in C

For certain applications, verifying the integrity of the data you’re sending and receiving can be very important. Because of this, the qik 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.

When the CRC jumper is in place, cyclic redundancy checking is enabled. In CRC mode, the qik 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 qik will set its CRC error bit in the error byte and ignore the command. The qik does not append a CRC byte to the data it sends back, which always consists of just one byte.

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 quick version is that a 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 qik uses CRC-7, which means it uses an 8-bit polynomial (whose most-significant bit, or MSB, must always be 1) 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 qik is the same as on the jrk motor controller but differs from that on the TReX motor controller. Instead of being done MSB first, it is 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 qik with CRC enabled).

If you’ve 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 (the command packet to get the PWM configuration parameter byte).


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 to retrieve the PWM configuration parameter with CRC enabled is: 0x83, 0x01, 0x17

There are some tricks you can use in your programs to make the CRC calculation much faster. You can find an example of this Section 6.a.