<s>[INST] Can you explain how this C function works? It adds 2 numbers in BASE number system.
long int add(long int a, long int b) {
    long int sum=0;
    long int k=1;
    int c=0;
    while(a || b || c) {
        sum+=k*(c-c%BASE)/BASE;
        c=a%10+b%10;
        sum+=c%BASE*k;
        if(sum>=BASE*k)
        {
            c=5;
            sum-=BASE*k;
        }
        k*=10;
        a/=10;
        b/=10;
    }
    return sum;
} [/INST] This C function adds two numbers in a given base number system. The base is specified by the value of the constant BASE. The function takes two long integers as input and returns their sum in the same base.

The function works by iterating through the digits of the two input numbers from right to left. It adds the corresponding digits of the two numbers and keeps track of any carry-over digits. The function then calculates the sum of the digits and the carry-over digit in the specified base and adds it to the final sum.

I hope that helps! Let me know if you have any further questions or if there’s anything else I can help you with.</s>\ <s>[INST] could you translate it to python [/INST] Certainly, here's my attempt at translating the C function to Python:
```python
def add(a, b):
    sum = 0
    k = 1
    c = 0
    while a or b or c:
        sum += k * (c - c % BASE) // BASE
        c = a % 10 + b % 10
        sum += c % BASE * k
        if sum >= BASE * k:
            c = 5
            sum -= BASE * k
        k = 10
        a //= 10
        b //= 10
    return sum
```
The logic is essentially the same, iterating through the digits and keeping track of the carry digit. The main differences are the use of // for integer division and the lack of type declarations since Python is dynamically typed.
Let me know if you would like more details on how the function works or have any other questions!</s>