Time and space complexity of Radix sort
A


  $k$ represented this number of digits of maximum value.


B


  k is the number of bits required to represent largest element in the array


This translates to number of digits required to represent the max value in binary. 

A is equivalent to B. 

Here is how: 

Say largest element in the array is 1233.

According to B, $k = log_2(1233) \approx 11$

According to A, $k = 4$, which is just $log_{10}(1233)$. 

There is formula for converting between the 
$$log_a(n) = \frac{log_b(n)}{log_b(a)}.$$

The denominator here $log_a(b)$ is a constant. 

So $log_2(n) = O(log_{10}(n))$. So it doesn't really matter to radix sort what base you are using.