# Системы счисления

## Теория

В системе счисления с основанием $$b$$ всего $$b$$ цифр, с числовыми значениями $${0,1,2,\dots, b-1}$$.

Число $$N$$ записывается цифрами $$d\_{n-1}d\_{n-2}\dots d\_2d\_1d\_0$$ в системе счисления с основанием $$b$$ означает, что $$N=d\_{n-1}\cdot b^{n-1} + d\_{n-2}\cdot b^{n-2}+\dots + d\_2\cdot b^2 + d\_1\cdot b^1 + d\_0\cdot b^0$$.

***

## Список цифр (любая СС)

### Перевод в СС

```python
def base(n, b):
    digits = []
    while n > 0:
        digits.append(n % b)
        n //= b
    return digits[::-1]
```

### Перевод из СС

```python
def number(digits, b):
    n = 0
    for digit in digits:
        n = n * b + digit
    return n
```

### Проверка функций

```python
for n in range(1, 1000):
    for b in range(2, 20):
        if n != number(base(n, b), b):
            print("ERROR")
```


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