对于特定的CRC实现，您需要“匹配”几个细节-即使使用相同的多项式，也可能会有不同的结果，因为数据位处理方式的微小差异，使用CRC的特定初始值（有时为零，有时为0xffff）和/或反转CRC的位。例如，有时一个实现将从数据字节的低阶位开始工作，而有时它们将从高阶位开始工作（就像您当前所做的那样）。
此外，您需要在运行所有数据位之后“推出”CRC的最后一位。
请记住，CRC算法被设计为在硬件中实现，因此从软件的Angular 来看，一些如何处理位排序的问题可能没有太大意义。
如果您想将CRC 16与多项式0x 8005匹配，如lammertbies.nl CRC计算器页面所示，则需要对CRC函数进行以下更改：

• a）从最低有效位而不是从最高有效位开始，使数据位通过CRC循环
• B）完成输入数据后，将CRC的最后16位从CRC寄存器中推出
• c）反转CRC位（我猜这个位是硬件实现的结转）

所以，你的函数可能看起来像这样：

#define CRC16 0x8005

uint16_t gen_crc16(const uint8_t *data, uint16_t size)
{
    uint16_t out = 0;
    int bits_read = 0, bit_flag;

    /* Sanity check: */
    if(data == NULL)
        return 0;

    while(size > 0)
    {
        bit_flag = out >> 15;

        /* Get next bit: */
        out <<= 1;
        out |= (*data >> bits_read) & 1; // item a) work from the least significant bits

        /* Increment bit counter: */
        bits_read++;
        if(bits_read > 7)
        {
            bits_read = 0;
            data++;
            size--;
        }

        /* Cycle check: */
        if(bit_flag)
            out ^= CRC16;

    }

    // item b) "push out" the last 16 bits
    int i;
    for (i = 0; i < 16; ++i) {
        bit_flag = out >> 15;
        out <<= 1;
        if(bit_flag)
            out ^= CRC16;
    }

    // item c) reverse the bits
    uint16_t crc = 0;
    i = 0x8000;
    int j = 0x0001;
    for (; i != 0; i >>=1, j <<= 1) {
        if (i & out) crc |= j;
    }

    return crc;
}

当我传入"123456789"时，该函数返回0xbb3d。

下面是计算crc16 CCITT的工作代码。我测试了它，结果与http://www.lammertbies.nl/comm/info/crc-calculation.html提供的结果相匹配。

unsigned short crc16(const unsigned char* data_p, unsigned char length){
    unsigned char x;
    unsigned short crc = 0xFFFF;

    while (length--){
        x = crc >> 8 ^ *data_p++;
        x ^= x>>4;
        crc = (crc << 8) ^ ((unsigned short)(x << 12)) ^ ((unsigned short)(x <<5)) ^ ((unsigned short)x);
    }
    return crc;
}

crcany将为任何CRC生成有效的C代码，并包含超过一百个已知CRC定义的库。
高效的CRC代码使用表格而不是逐位计算。crcany生成字节方式例程和字方式例程，后者被调整到它们在其上生成的体系结构。智慧是最快的。字节方式仍然比位方式快得多，但这种实现更容易在架构上移植。
您似乎没有需要匹配的具有特定CRC定义的协议定义。在这种情况下，您可以在catalog中选择任何16位CRC，并且您将获得良好的性能。
如果你有一个相对较低的误码率，例如，每个数据包的错误数为个位数，并且您希望最大化错误检测性能，则需要查看要应用CRC的数据包大小（假设该大小为常数或有界），并查看Philip Koopman's extensive research中最佳多项式的性能。经典的CRC，如CCITT/Kermit 16位CRC或X.25 16位CRC并不是性能最好的。
在Koopman的表中，CRC-16/DNP是一种性能良好的16位CRC，它也在实践中使用的CRC目录中。它具有非常好的性能，可以检测数据包中高达6位的错误。以下是crcany为CRC定义生成的代码。这段代码假设了一个小端体系结构来进行逐字计算，例如：Intel x86和x86-64，并假设uintmax_t是64位。CRCANY可用于生成用于大端字节序和其它字大小的替换代码。

• crc16dnp.h：*

// The _bit, _byte, and _word routines return the CRC of the len bytes at mem,
// applied to the previous CRC value, crc. If mem is NULL, then the other
// arguments are ignored, and the initial CRC, i.e. the CRC of zero bytes, is
// returned. Those routines will all return the same result, differing only in
// speed and code complexity. The _rem routine returns the CRC of the remaining
// bits in the last byte, for when the number of bits in the message is not a
// multiple of eight. The low bits bits of the low byte of val are applied to
// crc. bits must be in 0..8.

#include <stddef.h>

// Compute the CRC a bit at a time.
unsigned crc16dnp_bit(unsigned crc, void const *mem, size_t len);

// Compute the CRC of the low bits bits in val.
unsigned crc16dnp_rem(unsigned crc, unsigned val, unsigned bits);

// Compute the CRC a byte at a time.
unsigned crc16dnp_byte(unsigned crc, void const *mem, size_t len);

// Compute the CRC a word at a time.
unsigned crc16dnp_word(unsigned crc, void const *mem, size_t len);

• crc16dnp.c：*

#include <stdint.h>
#include "crc16dnp.h"

// This code assumes that unsigned is 4 bytes.

unsigned crc16dnp_bit(unsigned crc, void const *mem, size_t len) {
    unsigned char const *data = mem;
    if (data == NULL)
        return 0xffff;
    crc = ~crc;
    crc &= 0xffff;
    while (len--) {
        crc ^= *data++;
        for (unsigned k = 0; k < 8; k++)
            crc = crc & 1 ? (crc >> 1) ^ 0xa6bc : crc >> 1;
    }
    crc ^= 0xffff;
    return crc;
}

unsigned crc16dnp_rem(unsigned crc, unsigned val, unsigned bits) {
    crc = ~crc;
    crc &= 0xffff;
    val &= (1U << bits) - 1;
    crc ^= val;
    while (bits--)
        crc = crc & 1 ? (crc >> 1) ^ 0xa6bc : crc >> 1;
    crc ^= 0xffff;
    return crc;
}

#define table_byte table_word[0]

static unsigned short const table_word[][256] = {
   {0xed35, 0xdb6b, 0x8189, 0xb7d7, 0x344d, 0x0213, 0x58f1, 0x6eaf, 0x12bc, 0x24e2,
    0x7e00, 0x485e, 0xcbc4, 0xfd9a, 0xa778, 0x9126, 0x5f5e, 0x6900, 0x33e2, 0x05bc,
    0x8626, 0xb078, 0xea9a, 0xdcc4, 0xa0d7, 0x9689, 0xcc6b, 0xfa35, 0x79af, 0x4ff1,
    0x1513, 0x234d, 0xc49a, 0xf2c4, 0xa826, 0x9e78, 0x1de2, 0x2bbc, 0x715e, 0x4700,
    0x3b13, 0x0d4d, 0x57af, 0x61f1, 0xe26b, 0xd435, 0x8ed7, 0xb889, 0x76f1, 0x40af,
    0x1a4d, 0x2c13, 0xaf89, 0x99d7, 0xc335, 0xf56b, 0x8978, 0xbf26, 0xe5c4, 0xd39a,
    0x5000, 0x665e, 0x3cbc, 0x0ae2, 0xbe6b, 0x8835, 0xd2d7, 0xe489, 0x6713, 0x514d,
    0x0baf, 0x3df1, 0x41e2, 0x77bc, 0x2d5e, 0x1b00, 0x989a, 0xaec4, 0xf426, 0xc278,
    0x0c00, 0x3a5e, 0x60bc, 0x56e2, 0xd578, 0xe326, 0xb9c4, 0x8f9a, 0xf389, 0xc5d7,
    0x9f35, 0xa96b, 0x2af1, 0x1caf, 0x464d, 0x7013, 0x97c4, 0xa19a, 0xfb78, 0xcd26,
    0x4ebc, 0x78e2, 0x2200, 0x145e, 0x684d, 0x5e13, 0x04f1, 0x32af, 0xb135, 0x876b,
    0xdd89, 0xebd7, 0x25af, 0x13f1, 0x4913, 0x7f4d, 0xfcd7, 0xca89, 0x906b, 0xa635,
    0xda26, 0xec78, 0xb69a, 0x80c4, 0x035e, 0x3500, 0x6fe2, 0x59bc, 0x4b89, 0x7dd7,
    0x2735, 0x116b, 0x92f1, 0xa4af, 0xfe4d, 0xc813, 0xb400, 0x825e, 0xd8bc, 0xeee2,
    0x6d78, 0x5b26, 0x01c4, 0x379a, 0xf9e2, 0xcfbc, 0x955e, 0xa300, 0x209a, 0x16c4,
    0x4c26, 0x7a78, 0x066b, 0x3035, 0x6ad7, 0x5c89, 0xdf13, 0xe94d, 0xb3af, 0x85f1,
    0x6226, 0x5478, 0x0e9a, 0x38c4, 0xbb5e, 0x8d00, 0xd7e2, 0xe1bc, 0x9daf, 0xabf1,
    0xf113, 0xc74d, 0x44d7, 0x7289, 0x286b, 0x1e35, 0xd04d, 0xe613, 0xbcf1, 0x8aaf,
    0x0935, 0x3f6b, 0x6589, 0x53d7, 0x2fc4, 0x199a, 0x4378, 0x7526, 0xf6bc, 0xc0e2,
    0x9a00, 0xac5e, 0x18d7, 0x2e89, 0x746b, 0x4235, 0xc1af, 0xf7f1, 0xad13, 0x9b4d,
    0xe75e, 0xd100, 0x8be2, 0xbdbc, 0x3e26, 0x0878, 0x529a, 0x64c4, 0xaabc, 0x9ce2,
    0xc600, 0xf05e, 0x73c4, 0x459a, 0x1f78, 0x2926, 0x5535, 0x636b, 0x3989, 0x0fd7,
    0x8c4d, 0xba13, 0xe0f1, 0xd6af, 0x3178, 0x0726, 0x5dc4, 0x6b9a, 0xe800, 0xde5e,
    0x84bc, 0xb2e2, 0xcef1, 0xf8af, 0xa24d, 0x9413, 0x1789, 0x21d7, 0x7b35, 0x4d6b,
    0x8313, 0xb54d, 0xefaf, 0xd9f1, 0x5a6b, 0x6c35, 0x36d7, 0x0089, 0x7c9a, 0x4ac4,
    0x1026, 0x2678, 0xa5e2, 0x93bc, 0xc95e, 0xff00},
   {0x740f, 0xdf41, 0x6fea, 0xc4a4, 0x43c5, 0xe88b, 0x5820, 0xf36e, 0x1b9b, 0xb0d5,
    0x007e, 0xab30, 0x2c51, 0x871f, 0x37b4, 0x9cfa, 0xab27, 0x0069, 0xb0c2, 0x1b8c,
    0x9ced, 0x37a3, 0x8708, 0x2c46, 0xc4b3, 0x6ffd, 0xdf56, 0x7418, 0xf379, 0x5837,
    0xe89c, 0x43d2, 0x8726, 0x2c68, 0x9cc3, 0x378d, 0xb0ec, 0x1ba2, 0xab09, 0x0047,
    0xe8b2, 0x43fc, 0xf357, 0x5819, 0xdf78, 0x7436, 0xc49d, 0x6fd3, 0x580e, 0xf340,
    0x43eb, 0xe8a5, 0x6fc4, 0xc48a, 0x7421, 0xdf6f, 0x379a, 0x9cd4, 0x2c7f, 0x8731,
    0x0050, 0xab1e, 0x1bb5, 0xb0fb, 0xdf24, 0x746a, 0xc4c1, 0x6f8f, 0xe8ee, 0x43a0,
    0xf30b, 0x5845, 0xb0b0, 0x1bfe, 0xab55, 0x001b, 0x877a, 0x2c34, 0x9c9f, 0x37d1,
    0x000c, 0xab42, 0x1be9, 0xb0a7, 0x37c6, 0x9c88, 0x2c23, 0x876d, 0x6f98, 0xc4d6,
    0x747d, 0xdf33, 0x5852, 0xf31c, 0x43b7, 0xe8f9, 0x2c0d, 0x8743, 0x37e8, 0x9ca6,
    0x1bc7, 0xb089, 0x0022, 0xab6c, 0x4399, 0xe8d7, 0x587c, 0xf332, 0x7453, 0xdf1d,
    0x6fb6, 0xc4f8, 0xf325, 0x586b, 0xe8c0, 0x438e, 0xc4ef, 0x6fa1, 0xdf0a, 0x7444,
    0x9cb1, 0x37ff, 0x8754, 0x2c1a, 0xab7b, 0x0035, 0xb09e, 0x1bd0, 0x6f20, 0xc46e,
    0x74c5, 0xdf8b, 0x58ea, 0xf3a4, 0x430f, 0xe841, 0x00b4, 0xabfa, 0x1b51, 0xb01f,
    0x377e, 0x9c30, 0x2c9b, 0x87d5, 0xb008, 0x1b46, 0xabed, 0x00a3, 0x87c2, 0x2c8c,
    0x9c27, 0x3769, 0xdf9c, 0x74d2, 0xc479, 0x6f37, 0xe856, 0x4318, 0xf3b3, 0x58fd,
    0x9c09, 0x3747, 0x87ec, 0x2ca2, 0xabc3, 0x008d, 0xb026, 0x1b68, 0xf39d, 0x58d3,
    0xe878, 0x4336, 0xc457, 0x6f19, 0xdfb2, 0x74fc, 0x4321, 0xe86f, 0x58c4, 0xf38a,
    0x74eb, 0xdfa5, 0x6f0e, 0xc440, 0x2cb5, 0x87fb, 0x3750, 0x9c1e, 0x1b7f, 0xb031,
    0x009a, 0xabd4, 0xc40b, 0x6f45, 0xdfee, 0x74a0, 0xf3c1, 0x588f, 0xe824, 0x436a,
    0xab9f, 0x00d1, 0xb07a, 0x1b34, 0x9c55, 0x371b, 0x87b0, 0x2cfe, 0x1b23, 0xb06d,
    0x00c6, 0xab88, 0x2ce9, 0x87a7, 0x370c, 0x9c42, 0x74b7, 0xdff9, 0x6f52, 0xc41c,
    0x437d, 0xe833, 0x5898, 0xf3d6, 0x3722, 0x9c6c, 0x2cc7, 0x8789, 0x00e8, 0xaba6,
    0x1b0d, 0xb043, 0x58b6, 0xf3f8, 0x4353, 0xe81d, 0x6f7c, 0xc432, 0x7499, 0xdfd7,
    0xe80a, 0x4344, 0xf3ef, 0x58a1, 0xdfc0, 0x748e, 0xc425, 0x6f6b, 0x879e, 0x2cd0,
    0x9c7b, 0x3735, 0xb054, 0x1b1a, 0xabb1, 0x00ff},
   {0x7c67, 0x65df, 0x4f17, 0x56af, 0x1a87, 0x033f, 0x29f7, 0x304f, 0xb1a7, 0xa81f,
    0x82d7, 0x9b6f, 0xd747, 0xceff, 0xe437, 0xfd8f, 0xaa9e, 0xb326, 0x99ee, 0x8056,
    0xcc7e, 0xd5c6, 0xff0e, 0xe6b6, 0x675e, 0x7ee6, 0x542e, 0x4d96, 0x01be, 0x1806,
    0x32ce, 0x2b76, 0x9cec, 0x8554, 0xaf9c, 0xb624, 0xfa0c, 0xe3b4, 0xc97c, 0xd0c4,
    0x512c, 0x4894, 0x625c, 0x7be4, 0x37cc, 0x2e74, 0x04bc, 0x1d04, 0x4a15, 0x53ad,
    0x7965, 0x60dd, 0x2cf5, 0x354d, 0x1f85, 0x063d, 0x87d5, 0x9e6d, 0xb4a5, 0xad1d,
    0xe135, 0xf88d, 0xd245, 0xcbfd, 0xf008, 0xe9b0, 0xc378, 0xdac0, 0x96e8, 0x8f50,
    0xa598, 0xbc20, 0x3dc8, 0x2470, 0x0eb8, 0x1700, 0x5b28, 0x4290, 0x6858, 0x71e0,
    0x26f1, 0x3f49, 0x1581, 0x0c39, 0x4011, 0x59a9, 0x7361, 0x6ad9, 0xeb31, 0xf289,
    0xd841, 0xc1f9, 0x8dd1, 0x9469, 0xbea1, 0xa719, 0x1083, 0x093b, 0x23f3, 0x3a4b,
    0x7663, 0x6fdb, 0x4513, 0x5cab, 0xdd43, 0xc4fb, 0xee33, 0xf78b, 0xbba3, 0xa21b,
    0x88d3, 0x916b, 0xc67a, 0xdfc2, 0xf50a, 0xecb2, 0xa09a, 0xb922, 0x93ea, 0x8a52,
    0x0bba, 0x1202, 0x38ca, 0x2172, 0x6d5a, 0x74e2, 0x5e2a, 0x4792, 0x29c0, 0x3078,
    0x1ab0, 0x0308, 0x4f20, 0x5698, 0x7c50, 0x65e8, 0xe400, 0xfdb8, 0xd770, 0xcec8,
    0x82e0, 0x9b58, 0xb190, 0xa828, 0xff39, 0xe681, 0xcc49, 0xd5f1, 0x99d9, 0x8061,
    0xaaa9, 0xb311, 0x32f9, 0x2b41, 0x0189, 0x1831, 0x5419, 0x4da1, 0x6769, 0x7ed1,
    0xc94b, 0xd0f3, 0xfa3b, 0xe383, 0xafab, 0xb613, 0x9cdb, 0x8563, 0x048b, 0x1d33,
    0x37fb, 0x2e43, 0x626b, 0x7bd3, 0x511b, 0x48a3, 0x1fb2, 0x060a, 0x2cc2, 0x357a,
    0x7952, 0x60ea, 0x4a22, 0x539a, 0xd272, 0xcbca, 0xe102, 0xf8ba, 0xb492, 0xad2a,
    0x87e2, 0x9e5a, 0xa5af, 0xbc17, 0x96df, 0x8f67, 0xc34f, 0xdaf7, 0xf03f, 0xe987,
    0x686f, 0x71d7, 0x5b1f, 0x42a7, 0x0e8f, 0x1737, 0x3dff, 0x2447, 0x7356, 0x6aee,
    0x4026, 0x599e, 0x15b6, 0x0c0e, 0x26c6, 0x3f7e, 0xbe96, 0xa72e, 0x8de6, 0x945e,
    0xd876, 0xc1ce, 0xeb06, 0xf2be, 0x4524, 0x5c9c, 0x7654, 0x6fec, 0x23c4, 0x3a7c,
    0x10b4, 0x090c, 0x88e4, 0x915c, 0xbb94, 0xa22c, 0xee04, 0xf7bc, 0xdd74, 0xc4cc,
    0x93dd, 0x8a65, 0xa0ad, 0xb915, 0xf53d, 0xec85, 0xc64d, 0xdff5, 0x5e1d, 0x47a5,
    0x6d6d, 0x74d5, 0x38fd, 0x2145, 0x0b8d, 0x1235},
   {0xf917, 0x3bff, 0x31be, 0xf356, 0x253c, 0xe7d4, 0xed95, 0x2f7d, 0x0c38, 0xced0,
    0xc491, 0x0679, 0xd013, 0x12fb, 0x18ba, 0xda52, 0x5e30, 0x9cd8, 0x9699, 0x5471,
    0x821b, 0x40f3, 0x4ab2, 0x885a, 0xab1f, 0x69f7, 0x63b6, 0xa15e, 0x7734, 0xb5dc,
    0xbf9d, 0x7d75, 0xfa20, 0x38c8, 0x3289, 0xf061, 0x260b, 0xe4e3, 0xeea2, 0x2c4a,
    0x0f0f, 0xcde7, 0xc7a6, 0x054e, 0xd324, 0x11cc, 0x1b8d, 0xd965, 0x5d07, 0x9fef,
    0x95ae, 0x5746, 0x812c, 0x43c4, 0x4985, 0x8b6d, 0xa828, 0x6ac0, 0x6081, 0xa269,
    0x7403, 0xb6eb, 0xbcaa, 0x7e42, 0xff79, 0x3d91, 0x37d0, 0xf538, 0x2352, 0xe1ba,
    0xebfb, 0x2913, 0x0a56, 0xc8be, 0xc2ff, 0x0017, 0xd67d, 0x1495, 0x1ed4, 0xdc3c,
    0x585e, 0x9ab6, 0x90f7, 0x521f, 0x8475, 0x469d, 0x4cdc, 0x8e34, 0xad71, 0x6f99,
    0x65d8, 0xa730, 0x715a, 0xb3b2, 0xb9f3, 0x7b1b, 0xfc4e, 0x3ea6, 0x34e7, 0xf60f,
    0x2065, 0xe28d, 0xe8cc, 0x2a24, 0x0961, 0xcb89, 0xc1c8, 0x0320, 0xd54a, 0x17a2,
    0x1de3, 0xdf0b, 0x5b69, 0x9981, 0x93c0, 0x5128, 0x8742, 0x45aa, 0x4feb, 0x8d03,
    0xae46, 0x6cae, 0x66ef, 0xa407, 0x726d, 0xb085, 0xbac4, 0x782c, 0xf5cb, 0x3723,
    0x3d62, 0xff8a, 0x29e0, 0xeb08, 0xe149, 0x23a1, 0x00e4, 0xc20c, 0xc84d, 0x0aa5,
    0xdccf, 0x1e27, 0x1466, 0xd68e, 0x52ec, 0x9004, 0x9a45, 0x58ad, 0x8ec7, 0x4c2f,
    0x466e, 0x8486, 0xa7c3, 0x652b, 0x6f6a, 0xad82, 0x7be8, 0xb900, 0xb341, 0x71a9,
    0xf6fc, 0x3414, 0x3e55, 0xfcbd, 0x2ad7, 0xe83f, 0xe27e, 0x2096, 0x03d3, 0xc13b,
    0xcb7a, 0x0992, 0xdff8, 0x1d10, 0x1751, 0xd5b9, 0x51db, 0x9333, 0x9972, 0x5b9a,
    0x8df0, 0x4f18, 0x4559, 0x87b1, 0xa4f4, 0x661c, 0x6c5d, 0xaeb5, 0x78df, 0xba37,
    0xb076, 0x729e, 0xf3a5, 0x314d, 0x3b0c, 0xf9e4, 0x2f8e, 0xed66, 0xe727, 0x25cf,
    0x068a, 0xc462, 0xce23, 0x0ccb, 0xdaa1, 0x1849, 0x1208, 0xd0e0, 0x5482, 0x966a,
    0x9c2b, 0x5ec3, 0x88a9, 0x4a41, 0x4000, 0x82e8, 0xa1ad, 0x6345, 0x6904, 0xabec,
    0x7d86, 0xbf6e, 0xb52f, 0x77c7, 0xf092, 0x327a, 0x383b, 0xfad3, 0x2cb9, 0xee51,
    0xe410, 0x26f8, 0x05bd, 0xc755, 0xcd14, 0x0ffc, 0xd996, 0x1b7e, 0x113f, 0xd3d7,
    0x57b5, 0x955d, 0x9f1c, 0x5df4, 0x8b9e, 0x4976, 0x4337, 0x81df, 0xa29a, 0x6072,
    0x6a33, 0xa8db, 0x7eb1, 0xbc59, 0xb618, 0x74f0},
   {0x3108, 0x120e, 0x7704, 0x5402, 0xbd10, 0x9e16, 0xfb1c, 0xd81a, 0x6441, 0x4747,
    0x224d, 0x014b, 0xe859, 0xcb5f, 0xae55, 0x8d53, 0x9b9a, 0xb89c, 0xdd96, 0xfe90,
    0x1782, 0x3484, 0x518e, 0x7288, 0xced3, 0xedd5, 0x88df, 0xabd9, 0x42cb, 0x61cd,
    0x04c7, 0x27c1, 0x2955, 0x0a53, 0x6f59, 0x4c5f, 0xa54d, 0x864b, 0xe341, 0xc047,
    0x7c1c, 0x5f1a, 0x3a10, 0x1916, 0xf004, 0xd302, 0xb608, 0x950e, 0x83c7, 0xa0c1,
    0xc5cb, 0xe6cd, 0x0fdf, 0x2cd9, 0x49d3, 0x6ad5, 0xd68e, 0xf588, 0x9082, 0xb384,
    0x5a96, 0x7990, 0x1c9a, 0x3f9c, 0x01b2, 0x22b4, 0x47be, 0x64b8, 0x8daa, 0xaeac,
    0xcba6, 0xe8a0, 0x54fb, 0x77fd, 0x12f7, 0x31f1, 0xd8e3, 0xfbe5, 0x9eef, 0xbde9,
    0xab20, 0x8826, 0xed2c, 0xce2a, 0x2738, 0x043e, 0x6134, 0x4232, 0xfe69, 0xdd6f,
    0xb865, 0x9b63, 0x7271, 0x5177, 0x347d, 0x177b, 0x19ef, 0x3ae9, 0x5fe3, 0x7ce5,
    0x95f7, 0xb6f1, 0xd3fb, 0xf0fd, 0x4ca6, 0x6fa0, 0x0aaa, 0x29ac, 0xc0be, 0xe3b8,
    0x86b2, 0xa5b4, 0xb37d, 0x907b, 0xf571, 0xd677, 0x3f65, 0x1c63, 0x7969, 0x5a6f,
    0xe634, 0xc532, 0xa038, 0x833e, 0x6a2c, 0x492a, 0x2c20, 0x0f26, 0x507c, 0x737a,
    0x1670, 0x3576, 0xdc64, 0xff62, 0x9a68, 0xb96e, 0x0535, 0x2633, 0x4339, 0x603f,
    0x892d, 0xaa2b, 0xcf21, 0xec27, 0xfaee, 0xd9e8, 0xbce2, 0x9fe4, 0x76f6, 0x55f0,
    0x30fa, 0x13fc, 0xafa7, 0x8ca1, 0xe9ab, 0xcaad, 0x23bf, 0x00b9, 0x65b3, 0x46b5,
    0x4821, 0x6b27, 0x0e2d, 0x2d2b, 0xc439, 0xe73f, 0x8235, 0xa133, 0x1d68, 0x3e6e,
    0x5b64, 0x7862, 0x9170, 0xb276, 0xd77c, 0xf47a, 0xe2b3, 0xc1b5, 0xa4bf, 0x87b9,
    0x6eab, 0x4dad, 0x28a7, 0x0ba1, 0xb7fa, 0x94fc, 0xf1f6, 0xd2f0, 0x3be2, 0x18e4,
    0x7dee, 0x5ee8, 0x60c6, 0x43c0, 0x26ca, 0x05cc, 0xecde, 0xcfd8, 0xaad2, 0x89d4,
    0x358f, 0x1689, 0x7383, 0x5085, 0xb997, 0x9a91, 0xff9b, 0xdc9d, 0xca54, 0xe952,
    0x8c58, 0xaf5e, 0x464c, 0x654a, 0x0040, 0x2346, 0x9f1d, 0xbc1b, 0xd911, 0xfa17,
    0x1305, 0x3003, 0x5509, 0x760f, 0x789b, 0x5b9d, 0x3e97, 0x1d91, 0xf483, 0xd785,
    0xb28f, 0x9189, 0x2dd2, 0x0ed4, 0x6bde, 0x48d8, 0xa1ca, 0x82cc, 0xe7c6, 0xc4c0,
    0xd209, 0xf10f, 0x9405, 0xb703, 0x5e11, 0x7d17, 0x181d, 0x3b1b, 0x8740, 0xa446,
    0xc14c, 0xe24a, 0x0b58, 0x285e, 0x4d54, 0x6e52},
   {0xffb8, 0x4a5f, 0xd90f, 0x6ce8, 0xb2d6, 0x0731, 0x9461, 0x2186, 0x6564, 0xd083,
    0x43d3, 0xf634, 0x280a, 0x9ded, 0x0ebd, 0xbb5a, 0x8779, 0x329e, 0xa1ce, 0x1429,
    0xca17, 0x7ff0, 0xeca0, 0x5947, 0x1da5, 0xa842, 0x3b12, 0x8ef5, 0x50cb, 0xe52c,
    0x767c, 0xc39b, 0x0e3a, 0xbbdd, 0x288d, 0x9d6a, 0x4354, 0xf6b3, 0x65e3, 0xd004,
    0x94e6, 0x2101, 0xb251, 0x07b6, 0xd988, 0x6c6f, 0xff3f, 0x4ad8, 0x76fb, 0xc31c,
    0x504c, 0xe5ab, 0x3b95, 0x8e72, 0x1d22, 0xa8c5, 0xec27, 0x59c0, 0xca90, 0x7f77,
    0xa149, 0x14ae, 0x87fe, 0x3219, 0x51c5, 0xe422, 0x7772, 0xc295, 0x1cab, 0xa94c,
    0x3a1c, 0x8ffb, 0xcb19, 0x7efe, 0xedae, 0x5849, 0x8677, 0x3390, 0xa0c0, 0x1527,
    0x2904, 0x9ce3, 0x0fb3, 0xba54, 0x646a, 0xd18d, 0x42dd, 0xf73a, 0xb3d8, 0x063f,
    0x956f, 0x2088, 0xfeb6, 0x4b51, 0xd801, 0x6de6, 0xa047, 0x15a0, 0x86f0, 0x3317,
    0xed29, 0x58ce, 0xcb9e, 0x7e79, 0x3a9b, 0x8f7c, 0x1c2c, 0xa9cb, 0x77f5, 0xc212,
    0x5142, 0xe4a5, 0xd886, 0x6d61, 0xfe31, 0x4bd6, 0x95e8, 0x200f, 0xb35f, 0x06b8,
    0x425a, 0xf7bd, 0x64ed, 0xd10a, 0x0f34, 0xbad3, 0x2983, 0x9c64, 0xee3b, 0x5bdc,
    0xc88c, 0x7d6b, 0xa355, 0x16b2, 0x85e2, 0x3005, 0x74e7, 0xc100, 0x5250, 0xe7b7,
    0x3989, 0x8c6e, 0x1f3e, 0xaad9, 0x96fa, 0x231d, 0xb04d, 0x05aa, 0xdb94, 0x6e73,
    0xfd23, 0x48c4, 0x0c26, 0xb9c1, 0x2a91, 0x9f76, 0x4148, 0xf4af, 0x67ff, 0xd218,
    0x1fb9, 0xaa5e, 0x390e, 0x8ce9, 0x52d7, 0xe730, 0x7460, 0xc187, 0x8565, 0x3082,
    0xa3d2, 0x1635, 0xc80b, 0x7dec, 0xeebc, 0x5b5b, 0x6778, 0xd29f, 0x41cf, 0xf428,
    0x2a16, 0x9ff1, 0x0ca1, 0xb946, 0xfda4, 0x4843, 0xdb13, 0x6ef4, 0xb0ca, 0x052d,
    0x967d, 0x239a, 0x4046, 0xf5a1, 0x66f1, 0xd316, 0x0d28, 0xb8cf, 0x2b9f, 0x9e78,
    0xda9a, 0x6f7d, 0xfc2d, 0x49ca, 0x97f4, 0x2213, 0xb143, 0x04a4, 0x3887, 0x8d60,
    0x1e30, 0xabd7, 0x75e9, 0xc00e, 0x535e, 0xe6b9, 0xa25b, 0x17bc, 0x84ec, 0x310b,
    0xef35, 0x5ad2, 0xc982, 0x7c65, 0xb1c4, 0x0423, 0x9773, 0x2294, 0xfcaa, 0x494d,
    0xda1d, 0x6ffa, 0x2b18, 0x9eff, 0x0daf, 0xb848, 0x6676, 0xd391, 0x40c1, 0xf526,
    0xc905, 0x7ce2, 0xefb2, 0x5a55, 0x846b, 0x318c, 0xa2dc, 0x173b, 0x53d9, 0xe63e,
    0x756e, 0xc089, 0x1eb7, 0xab50, 0x3800, 0x8de7},
   {0xc20e, 0x9d6c, 0x7cca, 0x23a8, 0xf2ff, 0xad9d, 0x4c3b, 0x1359, 0xa3ec, 0xfc8e,
    0x1d28, 0x424a, 0x931d, 0xcc7f, 0x2dd9, 0x72bb, 0x01ca, 0x5ea8, 0xbf0e, 0xe06c,
    0x313b, 0x6e59, 0x8fff, 0xd09d, 0x6028, 0x3f4a, 0xdeec, 0x818e, 0x50d9, 0x0fbb,
    0xee1d, 0xb17f, 0x08ff, 0x579d, 0xb63b, 0xe959, 0x380e, 0x676c, 0x86ca, 0xd9a8,
    0x691d, 0x367f, 0xd7d9, 0x88bb, 0x59ec, 0x068e, 0xe728, 0xb84a, 0xcb3b, 0x9459,
    0x75ff, 0x2a9d, 0xfbca, 0xa4a8, 0x450e, 0x1a6c, 0xaad9, 0xf5bb, 0x141d, 0x4b7f,
    0x9a28, 0xc54a, 0x24ec, 0x7b8e, 0x1a95, 0x45f7, 0xa451, 0xfb33, 0x2a64, 0x7506,
    0x94a0, 0xcbc2, 0x7b77, 0x2415, 0xc5b3, 0x9ad1, 0x4b86, 0x14e4, 0xf542, 0xaa20,
    0xd951, 0x8633, 0x6795, 0x38f7, 0xe9a0, 0xb6c2, 0x5764, 0x0806, 0xb8b3, 0xe7d1,
    0x0677, 0x5915, 0x8842, 0xd720, 0x3686, 0x69e4, 0xd064, 0x8f06, 0x6ea0, 0x31c2,
    0xe095, 0xbff7, 0x5e51, 0x0133, 0xb186, 0xeee4, 0x0f42, 0x5020, 0x8177, 0xde15,
    0x3fb3, 0x60d1, 0x13a0, 0x4cc2, 0xad64, 0xf206, 0x2351, 0x7c33, 0x9d95, 0xc2f7,
    0x7242, 0x2d20, 0xcc86, 0x93e4, 0x42b3, 0x1dd1, 0xfc77, 0xa315, 0x3e41, 0x6123,
    0x8085, 0xdfe7, 0x0eb0, 0x51d2, 0xb074, 0xef16, 0x5fa3, 0x00c1, 0xe167, 0xbe05,
    0x6f52, 0x3030, 0xd196, 0x8ef4, 0xfd85, 0xa2e7, 0x4341, 0x1c23, 0xcd74, 0x9216,
    0x73b0, 0x2cd2, 0x9c67, 0xc305, 0x22a3, 0x7dc1, 0xac96, 0xf3f4, 0x1252, 0x4d30,
    0xf4b0, 0xabd2, 0x4a74, 0x1516, 0xc441, 0x9b23, 0x7a85, 0x25e7, 0x9552, 0xca30,
    0x2b96, 0x74f4, 0xa5a3, 0xfac1, 0x1b67, 0x4405, 0x3774, 0x6816, 0x89b0, 0xd6d2,
    0x0785, 0x58e7, 0xb941, 0xe623, 0x5696, 0x09f4, 0xe852, 0xb730, 0x6667, 0x3905,
    0xd8a3, 0x87c1, 0xe6da, 0xb9b8, 0x581e, 0x077c, 0xd62b, 0x8949, 0x68ef, 0x378d,
    0x8738, 0xd85a, 0x39fc, 0x669e, 0xb7c9, 0xe8ab, 0x090d, 0x566f, 0x251e, 0x7a7c,
    0x9bda, 0xc4b8, 0x15ef, 0x4a8d, 0xab2b, 0xf449, 0x44fc, 0x1b9e, 0xfa38, 0xa55a,
    0x740d, 0x2b6f, 0xcac9, 0x95ab, 0x2c2b, 0x7349, 0x92ef, 0xcd8d, 0x1cda, 0x43b8,
    0xa21e, 0xfd7c, 0x4dc9, 0x12ab, 0xf30d, 0xac6f, 0x7d38, 0x225a, 0xc3fc, 0x9c9e,
    0xefef, 0xb08d, 0x512b, 0x0e49, 0xdf1e, 0x807c, 0x61da, 0x3eb8, 0x8e0d, 0xd16f,
    0x30c9, 0x6fab, 0xbefc, 0xe19e, 0x0038, 0x5f5a},
   {0x4a8f, 0x5c9d, 0x66ab, 0x70b9, 0x12c7, 0x04d5, 0x3ee3, 0x28f1, 0xfa1f, 0xec0d,
    0xd63b, 0xc029, 0xa257, 0xb445, 0x8e73, 0x9861, 0x66d6, 0x70c4, 0x4af2, 0x5ce0,
    0x3e9e, 0x288c, 0x12ba, 0x04a8, 0xd646, 0xc054, 0xfa62, 0xec70, 0x8e0e, 0x981c,
    0xa22a, 0xb438, 0x123d, 0x042f, 0x3e19, 0x280b, 0x4a75, 0x5c67, 0x6651, 0x7043,
    0xa2ad, 0xb4bf, 0x8e89, 0x989b, 0xfae5, 0xecf7, 0xd6c1, 0xc0d3, 0x3e64, 0x2876,
    0x1240, 0x0452, 0x662c, 0x703e, 0x4a08, 0x5c1a, 0x8ef4, 0x98e6, 0xa2d0, 0xb4c2,
    0xd6bc, 0xc0ae, 0xfa98, 0xec8a, 0xfbeb, 0xedf9, 0xd7cf, 0xc1dd, 0xa3a3, 0xb5b1,
    0x8f87, 0x9995, 0x4b7b, 0x5d69, 0x675f, 0x714d, 0x1333, 0x0521, 0x3f17, 0x2905,
    0xd7b2, 0xc1a0, 0xfb96, 0xed84, 0x8ffa, 0x99e8, 0xa3de, 0xb5cc, 0x6722, 0x7130,
    0x4b06, 0x5d14, 0x3f6a, 0x2978, 0x134e, 0x055c, 0xa359, 0xb54b, 0x8f7d, 0x996f,
    0xfb11, 0xed03, 0xd735, 0xc127, 0x13c9, 0x05db, 0x3fed, 0x29ff, 0x4b81, 0x5d93,
    0x67a5, 0x71b7, 0x8f00, 0x9912, 0xa324, 0xb536, 0xd748, 0xc15a, 0xfb6c, 0xed7e,
    0x3f90, 0x2982, 0x13b4, 0x05a6, 0x67d8, 0x71ca, 0x4bfc, 0x5dee, 0x653e, 0x732c,
    0x491a, 0x5f08, 0x3d76, 0x2b64, 0x1152, 0x0740, 0xd5ae, 0xc3bc, 0xf98a, 0xef98,
    0x8de6, 0x9bf4, 0xa1c2, 0xb7d0, 0x4967, 0x5f75, 0x6543, 0x7351, 0x112f, 0x073d,
    0x3d0b, 0x2b19, 0xf9f7, 0xefe5, 0xd5d3, 0xc3c1, 0xa1bf, 0xb7ad, 0x8d9b, 0x9b89,
    0x3d8c, 0x2b9e, 0x11a8, 0x07ba, 0x65c4, 0x73d6, 0x49e0, 0x5ff2, 0x8d1c, 0x9b0e,
    0xa138, 0xb72a, 0xd554, 0xc346, 0xf970, 0xef62, 0x11d5, 0x07c7, 0x3df1, 0x2be3,
    0x499d, 0x5f8f, 0x65b9, 0x73ab, 0xa145, 0xb757, 0x8d61, 0x9b73, 0xf90d, 0xef1f,
    0xd529, 0xc33b, 0xd45a, 0xc248, 0xf87e, 0xee6c, 0x8c12, 0x9a00, 0xa036, 0xb624,
    0x64ca, 0x72d8, 0x48ee, 0x5efc, 0x3c82, 0x2a90, 0x10a6, 0x06b4, 0xf803, 0xee11,
    0xd427, 0xc235, 0xa04b, 0xb659, 0x8c6f, 0x9a7d, 0x4893, 0x5e81, 0x64b7, 0x72a5,
    0x10db, 0x06c9, 0x3cff, 0x2aed, 0x8ce8, 0x9afa, 0xa0cc, 0xb6de, 0xd4a0, 0xc2b2,
    0xf884, 0xee96, 0x3c78, 0x2a6a, 0x105c, 0x064e, 0x6430, 0x7222, 0x4814, 0x5e06,
    0xa0b1, 0xb6a3, 0x8c95, 0x9a87, 0xf8f9, 0xeeeb, 0xd4dd, 0xc2cf, 0x1021, 0x0633,
    0x3c05, 0x2a17, 0x4869, 0x5e7b, 0x644d, 0x725f}
};

unsigned crc16dnp_byte(unsigned crc, void const *mem, size_t len) {
    unsigned char const *data = mem;
    if (data == NULL)
        return 0xffff;
    crc &= 0xffff;
    while (len--)
        crc = (crc >> 8) ^
              table_byte[(crc ^ *data++) & 0xff];
    return crc;
}

// This code assumes that integers are stored little-endian.

unsigned crc16dnp_word(unsigned crc, void const *mem, size_t len) {
    unsigned char const *data = mem;
    if (data == NULL)
        return 0xffff;
    crc &= 0xffff;
    while (len && ((ptrdiff_t)data & 0x7)) {
        crc = (crc >> 8) ^
              table_byte[(crc ^ *data++) & 0xff];
        len--;
    }
    if (len >= 8) {
        do {
            uintmax_t word = crc ^ *(uintmax_t const *)data;
            crc = table_word[7][word & 0xff] ^
                  table_word[6][(word >> 8) & 0xff] ^
                  table_word[5][(word >> 16) & 0xff] ^
                  table_word[4][(word >> 24) & 0xff] ^
                  table_word[3][(word >> 32) & 0xff] ^
                  table_word[2][(word >> 40) & 0xff] ^
                  table_word[1][(word >> 48) & 0xff] ^
                  table_word[0][word >> 56];
            data += 8;
            len -= 8;
        } while (len >= 8);
    }
    while (len--)
        crc = (crc >> 8) ^
              table_byte[(crc ^ *data++) & 0xff];
    return crc;
}

CRC-16有几个不同的品种。请参见wiki page。
每一个都将从相同的输入返回不同的结果。
所以你必须仔细选择一个正确的程序。

for (pos = 0; pos < len; pos++) {
    crc ^= (uint16_t)buf[pos];     // XOR byte into least sig. byte of crc

    for (i = 8; i != 0; i--) {     // Loop over each bit
        if ((crc & 0x0001) != 0) { // If the LSB is set
            crc >>= 1;             // Shift right and XOR 0xA001
            crc ^= CRC16;
        } else {                   // Else LSB is not set
            crc >>= 1;             // Just shift right
        }
     }
}

return crc;

我使用的代码示例来自：http://www.sunshine2k.de/articles/coding/crc/understanding_crc.html#ch5
还有这个实用程序来验证：http://www.sunshine2k.de/coding/javascript/crc/crc_js.html

为了生成数据包的校验和，例如该数据包“78781101086655103641220800002122000fdcfd0d0a”“dcfd”，这是错误校验和，这是由“1101086655103641220800002122000f”生成的，这些人误解了生成“dcfd”的响应校验和。但是校验和是通过使用其自己的分组数据来生成的。
7878和odoa是固定的，所以..

package org.traccar.helper;

import java.nio.ByteBuffer;
import java.nio.charset.StandardCharsets;
import java.util.zip.CRC32;

public final class Checksum {

    private Checksum() {
    }

    public static class Algorithm {

        private final int poly;
        private final int init;
        private final boolean refIn;
        private final boolean refOut;
        private final int xorOut;
        private final int[] table;

        public Algorithm(int bits, int poly, int init, boolean refIn, boolean refOut, int xorOut) {
            this.poly = poly;
            this.init = init;
            this.refIn = refIn;
            this.refOut = refOut;
            this.xorOut = xorOut;
            this.table = bits == 8 ? initTable8() : initTable16();
        }

        private int[] initTable8() {
            int[] table = new int[256];
            int crc;
            for (int i = 0; i < 256; i++) {
                crc = i;
                for (int j = 0; j < 8; j++) {
                    boolean bit = (crc & 0x80) != 0;
                    crc <<= 1;
                    if (bit) {
                        crc ^= poly;
                    }
                }
                table[i] = crc & 0xFF;
            }
            return table;
        }

        private int[] initTable16() {
            int[] table = new int[256];
            int crc;
            for (int i = 0; i < 256; i++) {
                crc = i << 8;
                for (int j = 0; j < 8; j++) {
                    boolean bit = (crc & 0x8000) != 0;
                    crc <<= 1;
                    if (bit) {
                        crc ^= poly;
                    }
                }
                table[i] = crc & 0xFFFF;
            }
            return table;
        }

    }

    private static int reverse(int value, int bits) {
        int result = 0;
        for (int i = 0; i < bits; i++) {
            result = (result << 1) | (value & 1);
            value >>= 1;
        }
        return result;
    }

    public static int crc8(Algorithm algorithm, ByteBuffer buf) {
        int crc = algorithm.init;
        while (buf.hasRemaining()) {
            int b = buf.get() & 0xFF;
            if (algorithm.refIn) {
                b = reverse(b, 8);
            }
            crc = algorithm.table[(crc & 0xFF) ^ b];
        }
        if (algorithm.refOut) {
            crc = reverse(crc, 8);
        }
        return (crc ^ algorithm.xorOut) & 0xFF;
    }

    public static int crc16(Algorithm algorithm, ByteBuffer buf) {
        int crc = algorithm.init;
        while (buf.hasRemaining()) {
            int b = buf.get() & 0xFF;
            if (algorithm.refIn) {
                b = reverse(b, 8);
            }
            crc = (crc << 8) ^ algorithm.table[((crc >> 8) & 0xFF) ^ b];
        }
        if (algorithm.refOut) {
            crc = reverse(crc, 16);
        }
        return (crc ^ algorithm.xorOut) & 0xFFFF;
    }

    public static final Algorithm CRC8_EGTS = new Algorithm(8, 0x31, 0xFF, false, false, 0x00);
    public static final Algorithm CRC8_ROHC = new Algorithm(8, 0x07, 0xFF, true, true, 0x00);

    public static final Algorithm CRC16_IBM = new Algorithm(16, 0x8005, 0x0000, true, true, 0x0000);
    public static final Algorithm CRC16_X25 = new Algorithm(16, 0x1021, 0xFFFF, true, true, 0xFFFF);
    public static final Algorithm CRC16_MODBUS = new Algorithm(16, 0x8005, 0xFFFF, true, true, 0x0000);
    public static final Algorithm CRC16_CCITT_FALSE = new Algorithm(16, 0x1021, 0xFFFF, false, false, 0x0000);
    public static final Algorithm CRC16_KERMIT = new Algorithm(16, 0x1021, 0x0000, true, true, 0x0000);
    public static final Algorithm CRC16_XMODEM = new Algorithm(16, 0x1021, 0x0000, false, false, 0x0000);

    public static int crc32(ByteBuffer buf) {
        CRC32 checksum = new CRC32();
        while (buf.hasRemaining()) {
            checksum.update(buf.get());
        }
        return (int) checksum.getValue();
    }

    public static int xor(ByteBuffer buf) {
        int checksum = 0;
        while (buf.hasRemaining()) {
            checksum ^= buf.get();
        }
        return checksum;
    }

    public static int xor(String string) {
        byte checksum = 0;
        for (byte b : string.getBytes(StandardCharsets.US_ASCII)) {
            checksum ^= b;
        }
        return checksum;
    }

    public static String nmea(String string) {
        return String.format("*%02X", xor(string));
    }

    public static int sum(ByteBuffer buf) {
        byte checksum = 0;
        while (buf.hasRemaining()) {
            checksum += buf.get();
        }
        return checksum;
    }

    public static int modulo256(ByteBuffer buf) {
        int checksum = 0;
        while (buf.hasRemaining()) {
            checksum = (checksum + buf.get()) & 0xFF;
        }
        return checksum;
    }

    public static String sum(String msg) {
        byte checksum = 0;
        for (byte b : msg.getBytes(StandardCharsets.US_ASCII)) {
            checksum += b;
        }
        return String.format("%02X", checksum).toUpperCase();
    }

    public static long luhn(long imei) {
        long checksum = 0;
        long remain = imei;

        for (int i = 0; remain != 0; i++) {
            long digit = remain % 10;

            if (i % 2 == 0) {
                digit *= 2;
                if (digit >= 10) {
                    digit = 1 + (digit % 10);
                }
            }

            checksum += digit;
            remain /= 10;
        }

        return (10 - (checksum % 10)) % 10;
    }

    public static int ip(ByteBuffer data) {
        int sum = 0;
        while (data.remaining() > 0) {
            sum += data.get() & 0xff;
            if ((sum & 0x80000000) > 0) {
                sum = (sum & 0xffff) + (sum >> 16);
            }
        }
        while ((sum >> 16) > 0) {
            sum = (sum & 0xffff) + sum >> 16;
        }
        sum = (sum == 0xffff) ? sum & 0xffff : (~sum) & 0xffff;
        return sum;
    }

}

检查你的代码使用这个作为一个例子“78781101086655103641220800002122000fdcfd0d0a”通过它“1101086655103641220800002122000f”和它的答案是“dcfd”意味着你的代码工作正常
ignore 8a51这只是为了检查不要担心帮助：email protected(https://stackoverflow.com/cdn-cgi/l/email-protection)
在checksumExample和boom中导入此校验和
我的校验和是在org.traccar.helper文件夹..

`enter code here`package org.traccar.helper;

import java.nio.ByteBuffer;

public class ChecksumExample {

    public static void main(String[] args) {
        // Convert the hexadecimal string to a byte array
        String hexData = "1101086655103641220800002122000f";
        byte[] dataBytes = hexStringToByteArray(hexData);

        // Create a ByteBuffer from the byte array
        ByteBuffer buf = ByteBuffer.wrap(dataBytes);

        // Use the CRC-16 algorithm
        int crcValue = Checksum.crc16(Checksum.CRC16_X25, buf);

        // Convert the expected checksum "8a51" to an integer
        int expectedChecksum = Integer.parseInt("8a51", 16);

        // Verify the checksum
        boolean checksumMatch = crcValue == expectedChecksum;

        System.out.println("Generated CRC-16: " + Integer.toHexString(crcValue));
        System.out.println("Expected CRC-16: " + Integer.toHexString(expectedChecksum));
        System.out.println("Checksum Match: " + checksumMatch);
    }

    // Helper method to convert a hexadecimal string to a byte array
    private static byte[] hexStringToByteArray(String hex) {
        int len = hex.length();
        byte[] data = new byte[len / 2];
        for (int i = 0; i < len; i += 2) {
            data[i / 2] = (byte) ((Character.digit(hex.charAt(i), 16) << 4)
                    + Character.digit(hex.charAt(i + 1), 16));
        }
        return data;
    }
}

``