### AN-1251: ADAS1000 Cyclic Redundancy Code (Rev. 0) PDF

```AN-1251
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
INTRODUCTION
This application note details the ADAS1000 cyclic redundancy
code. The aim of error detection is to enable the receiver of a
message to determine whether the message has been corrupted.
To do this, the ADAS1000 constructs a code (called a
checksum) that is a function of the message and appends it
to the message.
The CRC algorithms simply treat the message as an enormous
polynomial, dividing it by another fixed polynomial using
Modulo 2 arithmetic for the coefficients, and making the
remainder from this division the checksum. Upon receipt of
the message, the receiver can perform the same division and
compare the remainder with the checksum.
This application note describes how the code (checksum) for
Rev. 0 | Page 1 of 8
AN-1251
Application Note
Introduction ...................................................................................... 1
Computing the CRC Using the ADAS1000 ...............................3
Revision History ............................................................................... 2
Verifying the CRC on the Receiver Side ....................................5
Cyclic Redundancy Code ................................................................ 3
REVISION HISTORY
3/14—Revision 0: Initial Version
Rev. 0 | Page 2 of 8
Application Note
AN-1251
CYCLIC REDUNDANCY CODE
COMPUTING THE CRC USING THE ADAS1000
For each bit in the message, a series of six steps occurs.
128 kHz Data Rate Example
1.
For a 128 kHz data rate, the polynomial used is
2.
3.
x16 + x12 + x5 + x0
This is also known as the CRC-16-CCITT polynomial.
4.
0x11021 (polynomial: 10001000000100001).
The ADAS1000 presets the CRC register to all ones (0xFFFF)
where the CRC register is 1111111111111111.
5.
For each data bit (below for 16-bits), the remainder shifts
left by one.
The MSB of the remainder is XOR’d with the data bit.
If the resulting MSB is 1, the remainder is then XOR’d with
the polynomial.
If the resulting MSB is 0, the remainder is not XOR’d with
the polynomial.
Repeat Step 1 through Step 4 for each data bit.
Note that data bits are shifted MSB first.
The result in the CRC register, after all message bits are shifted
through the register as described, is the CRC code.
For example, when transmitting the header only using the
0x8000 (1000000000000000).
1111111111111111
initial CRC is pre-set all ones
< 11111111111111110 shift CRC
^ 1
XOR with data bit 15
= 1111111111111110 CRC after data bit 15
<
^
=
^
=
11111111111111100
0
11111111111111100
10001000000100001
1110111111011101
<
^
=
^
=
11101111110111010
0
11101111110111010
10001000000100001
1100111110011011
<
^
=
^
=
11001111100110110
0
11001111100110110
10001000000100001
1000111100010111
<
^
=
^
=
10001111000101110
0
10001111000101110
10001000000100001
0000111000001111
shift CRC
XOR with data bit 14
XOR with poly
CRC after data bit 14
shift CRC
XOR with data bit 13
XOR with poly
CRC after data bit 13
shift CRC
XOR with data bit 12
XOR with poly
CRC after data bit 12
shift CRC
XOR with data bit 11
XOR with poly
CRC after data bit 11
< 00001110000011110 shift CRC
^ 0
XOR with data bit 10
= 0001110000011110 CRC after data bit 10
< 00011100000111100 shift CRC
^ 0
XOR with data bit 9
= 0011100000111100 CRC after data bit 9
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AN-1251
Application Note
< 00111000001111000 shift CRC
^ 0
XOR with data bit 8
= 0111000001111000 CRC after data bit 8
< 01110000011110000 shift CRC
^ 0
XOR with data bit 7
= 1110000011110000 CRC after data bit 7
<
^
=
^
=
11100000111100000
0
11100000111100000
10001000000100001
1101000111000001
<
^
=
^
=
11010001110000010
0
11010001110000010
10001000000100001
1011001110100011
<
^
=
^
=
10110011101000110
0
10110011101000110
10001000000100001
0111011101100111
shift CRC
XOR with data bit 6
XOR with poly
CRC after data bit 6
shift CRC
XOR with data bit 5
XOR with poly
CRC after data bit 5
shift CRC
XOR with data bit 4
XOR with poly
CRC after data bit 4
< 01110111011001110 shift CRC
^ 0
XOR with data bit 3
= 1110111011001110 CRC after data bit 3
<
^
=
^
=
11101110110011100
0
11101110110011100
10001000000100001
1100110110111101
<
^
=
^
=
11001101101111010
0
11001101101111010
10001000000100001
1000101101011011
<
^
=
^
=
10001011010110110
0
10001011010110110
10001000000100001
0000011010010111
shift CRC
XOR with data bit 2
XOR with poly
CRC after data bit 2
shift CRC
XOR with data bit 1
XOR with poly
CRC after data bit 1
shift CRC
XOR with data bit 0
XOR with poly
CRC after data bit 0
In this example, the CRC result is 0x0697.
The ADAS1000 inverts message 0x0697 (0000011010010111)
before transmission, as stated in the data sheet, and the message
becomes 0xF968 (1111100101101000).
The full transmission should contain 0x8000F968. The message
is appended by the CRC.
Rev. 0 | Page 4 of 8
Application Note
AN-1251
VERIFYING THE CRC ON THE RECEIVER SIDE
128 kHz Data Rate Example
To verify that data was correctly received, the software should
compute a CRC on both the data and the received checksum.
1111111111111111
The same steps (Step 1 through Step 5 in the Computing the
CRC Using the ADAS1000 section) are applied to the each data
(10000000000000001111100101101000).
initial CRC is pre-set all ones
< 11111111111111110 shift CRC
^ 1
XOR with data bit 31
= 1111111111111110 CRC after data bit 31
<
^
=
^
=
11111111111111100
0
11111111111111100
10001000000100001
1110111111011101
shift CRC
XOR with data bit 30
<
^
=
^
=
11101111110111010
0
11101111110111010
10001000000100001
1100111110011011
shift CRC
XOR with data bit 29
<
^
=
^
=
11001111100110110
0
11001111100110110
10001000000100001
1000111100010111
shift CRC
XOR with data bit 28
<
^
=
^
=
10001111000101110
0
10001111000101110
10001000000100001
0000111000001111
XOR with poly
CRC after data bit 30
XOR with poly
CRC after data bit 29
XOR with poly
CRC after data bit 28
shift CRC
XOR with data bit 27
XOR with poly
CRC after data bit 27
< 00001110000011110 shift CRC
^ 0
XOR with data bit 26
= 0001110000011110 CRC after data bit 26
< 00011100000111100 shift CRC
^ 0
XOR with data bit 25
= 0011100000111100 CRC after data bit 25
< 00111000001111000 shift CRC
^ 0
XOR with data bit 24
= 0111000001111000 CRC after data bit 24
< 01110000011110000 shift CRC
^ 0
XOR with data bit 23
= 1110000011110000 CRC after data bit 23
<
^
=
^
=
11100000111100000
0
11100000111100000
10001000000100001
1101000111000001
shift CRC
XOR with data bit 22
XOR with poly
CRC after data bit 22
< 11010001110000010 shift CRC
Rev. 0 | Page 5 of 8
AN-1251
Application Note
^ 0
XOR with data bit 21
= 11010001110000010
^ 10001000000100001 XOR with poly
= 1011001110100011 CRC after data bit 21
<
^
=
^
=
10110011101000110
0
10110011101000110
10001000000100001
0111011101100111
shift CRC
XOR with data bit 20
XOR with poly
CRC after data bit 20
< 01110111011001110 shift CRC
^ 0
XOR with data bit 19
= 1110111011001110 CRC after data bit 19
<
^
=
^
=
11101110110011100
0
11101110110011100
10001000000100001
1100110110111101
shift CRC
XOR with data bit 18
<
^
=
^
=
11001101101111010
0
11001101101111010
10001000000100001
1000101101011011
shift CRC
XOR with data bit 17
<
^
=
^
=
10001011010110110
0
10001011010110110
10001000000100001
0000011010010111
shift CRC
XOR with data bit 16
<
^
=
^
=
00000110100101110
1
10000110100101110
10001000000100001
0001110100001111
shift CRC
XOR with RX CRC bit 15
<
^
=
^
=
00011101000011110
1
10011101000011110
10001000000100001
0010101000111111
shift CRC
XOR with RX CRC bit 14
<
^
=
^
=
00101010001111110
1
10101010001111110
10001000000100001
0100010001011111
shift CRC
XOR with RX CRC bit 13
<
^
=
^
=
01000100010111110
1
11000100010111110
10001000000100001
1001100010011111
shift CRC
XOR with RX CRC bit 12
XOR with poly
CRC after data bit 18
XOR with poly
CRC after data bit 17
XOR with poly
CRC after data bit 16
XOR with poly
CRC after RX CRC bit 15
XOR with poly
CRC after RX CRC bit 14
XOR with poly
CRC after RX CRC bit 13
XOR with poly
CRC after RX CRC bit 12
< 10011000100111110 shift CRC
^ 1
XOR with RX CRC bit 11
= 0011000100111110 CRC after RX CRC bit 11
Rev. 0 | Page 6 of 8
Application Note
AN-1251
< 00110001001111100 shift CRC
^ 0
XOR with RX CRC bit 10
= 0110001001111100 CRC after RX CRC bit 10
< 01100010011111000 shift CRC
^ 0
XOR with RX CRC bit 9
= 1100010011111000 CRC after RX CRC bit 9
< 11000100111110000 shift CRC
^ 1
XOR with RX CRC bit 8
= 1000100111110000 CRC after RX CRC bit 8
<
^
=
^
=
10001001111100000
0
10001001111100000
10001000000100001
0000001111000001
shift CRC
XOR with RX CRC bit 7
<
^
=
^
=
00000011110000010
1
10000011110000010
10001000000100001
0001011110100011
shift CRC
XOR with RX CRC bit 6
<
^
=
^
=
00010111101000110
1
10010111101000110
10001000000100001
0011111101100111
shift CRC
XOR with RX CRC bit 5
XOR with poly
CRC after RX CRC bit 7
XOR with poly
CRC after RX CRC bit 6
XOR with poly
CRC after RX CRC bit 5
< 00111111011001110 shift CRC
^ 0
XOR with RX CRC bit 4
= 0111111011001110 CRC after RX CRC bit 4
<
^
=
^
=
01111110110011100
1
11111110110011100
10001000000100001
1110110110111101
shift CRC
XOR with RX CRC bit 3
<
^
=
^
=
11101101101111010
0
11101101101111010
10001000000100001
1100101101011011
shift CRC
XOR with RX CRC bit 2
<
^
=
^
=
11001011010110110
0
11001011010110110
10001000000100001
1000011010010111
shift CRC
XOR with RX CRC bit 1
<
^
=
^
=
10000110100101110
0
10000110100101110
10001000000100001
0001110100001111
shift CRC
XOR with RX CRC bit 0
XOR with poly
CRC after RX CRC bit 3
XOR with poly
CRC after RX CRC bit 2
XOR with poly
CRC after RX CRC bit 1
XOR with poly
CRC after RX CRC bit 0
If the CRC is correct, the remainder on the receive side equals 0x1D0F, the check constant.
Rev. 0 | Page 7 of 8
AN-1251
Application Note
2 kHz and 16 kHz Data Rate Examples
For 2 kHz and 16 kHz data rates, the polynomial used is
Note that data bits are shifted MSB first.
x +x +x +x +x +x +x +x +x +x +x +x
+ x6 + x3 + x1 + x0
24
22
20
19
18
16
14
13
11
10
8
7
The ADAS1000 inverts message CRC before transmission, as
stated in the data sheet, and the message becomes the data and
the inverted CRC.
This is also known as the 24-bit CRC polynomial.
0x15D6DCB (polynomial: 1010111010110110111001011).
The ADAS1000 presets the CRC register to all ones (0xFFFFFF)
where the CRC register is 111111111111111111111111.
For each bit in the message, a series of steps occurs.
1.
2.
3.
4.
5.
The result in the CRC register, after all message bits are shifted
through the register as described, is the CRC code.
For each data bit, the remainder shifts left by one.
The MSB of the remainder is XOR’d with the data bit.
If the resulting MSB is 1, the remainder is then XOR’d with
the polynomial.
If the resulting MSB is 0, the remainder is not XOR’d with
the polynomial.
Repeat Step 1 through Step 4 for each data bit.
To verify that data was correctly received, the software should
compute a CRC on both the data and the received checksum.
The same steps are applied to each data bit and received
checksum and data.
If the CRC is correct, the remainder on the receive side equals
0x15A0BA, the check constant.