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#technique used to detect error
#algo
#1. we have message bits and crc generator given to us

message= input("Enter message:")
crc= input("Enter crc:")
len_crc= len(crc)

#2. append (n-1) 0's where n is the no. of bits in crc generator to the message
temp= message+'0'*(len_crc-1)
#print(temp)

#3. perform xor operation(division by 2) on crc and temp
#find index in temp for 1's '1' from left
def find_index(temp):
    length= len(temp)
    i=0
    while i<length and temp[i]=='0':
        i+=1

    return i

def solve(temp,crc):
    #perform one time xor operation before.
    #It is because when we perform xor operation first time
    #then irrespective of the 1st bit(either 0 or 1) in temp we have to perform xor operation.
    #After that, xor operation is performed with respect to first 1 from left.
    xor(temp,0,crc)
    #print(temp)

    #find index in temp for first '1' from left
    index= find_index(temp)
    #print(index)

    #length= len(temp)

    while len(temp[index:])>=len_crc:
        
        #print(index)

        #we need to perform xor operation till we have 4 bits left
        #if index+4<len
        xor(temp,index,crc)


        #find index in temp for first '1' from left
        index= find_index(temp)
        #print(index)

    #print(temp)
    #return the bits to be appended to the actual message
    result= temp[index:]
    #no. of zeros to add
    n_zero= len_crc-1-len(result)
    for i in range(n_zero): result.append('0')

    return result
    

def xor(temp, index, crc):
    i=0
    j= index
    while i<len_crc:
        if crc[i]==temp[j]:
            temp[j]= '0'
        else:
            temp[j]= '1'
        j+=1
        i+=1
    

#convert temp to a list
#because string is immutable
temp= [char for char in temp]

#bits to be added at the end of actual message
add_bits= ''.join(solve(temp, crc))

#message bits sent to receiver
receiver= message+add_bits

print(receiver)