Alex Stewart Alex Stewart - 1 year ago 282
Python Question

CRC-CCITT 16-bit Python Manual Calculation


I am writing code for an embedded device. A lot of solutions out there for CRC-CCITT 16-bit calculations require libraries.

Given that using libraries is almost impossible and a drain on its resources, a function is required.

Possible Solution

The following CRC calculation was found online. However, its implementation is incorrect.

def checkCRC(message):
#CRC-16-CITT poly, the CRC sheme used by ymodem protocol
poly = 0x11021
#16bit operation register, initialized to zeros
reg = 0xFFFF
#pad the end of the message with the size of the poly
message += '\x00\x00'
#for each bit in the message
for byte in message:
mask = 0x80
while(mask > 0):
#left shift by one
#input the next bit from the message into the right hand side of the op reg
if ord(byte) & mask:
reg += 1
#if a one popped out the left of the reg, xor reg w/poly
if reg > 0xffff:
#eliminate any one that popped out the left
reg &= 0xffff
#xor with the poly, this is the remainder
reg ^= poly
return reg

Existing Online Solution

The following link calculates a 16 bit CRC correctly.

The result under "CRC-CCITT (XModem)" is the correct CRC.


I believe the "CRC-CCITT (XModem)" calculation in the existing online solution uses a polynomial of


If someone could write a new function or provide direction to solve the
function to the required specification. Please note that the use of libraries or any
's would not help.

Answer Source

Here is a python port of the C library from for CRC-CCITT XMODEM

This library is interesting for real use cases because it pre-computes a table of crc for enhanced speed.

Usage (with a string or a list of bytes) :

crcb(0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39)

The test gives : '0x31c3'


def _initial(c):
    crc = 0
    c = c << 8
    for j in range(8):
        if (crc ^ c) & 0x8000:
            crc = (crc << 1) ^ POLYNOMIAL
            crc = crc << 1
        c = c << 1
    return crc

_tab = [ _initial(i) for i in range(256) ]

def _update_crc(crc, c):
    cc = 0xff & c

    tmp = (crc >> 8) ^ cc
    crc = (crc << 8) ^ _tab[tmp & 0xff]
    crc = crc & 0xffff
    print (crc)

    return crc

def crc(str):
    crc = PRESET
    for c in str:
        crc = _update_crc(crc, ord(c))
    return crc

def crcb(*i):
    crc = PRESET
    for c in i:
        crc = _update_crc(crc, c)
    return crc

Your proposed checkCRC routine is CRC-CCITT variant '1D0F' if you replace poly = 0x11021 with poly = 0x1021 at the beginning.