Does time or space complexity of arithmetic operations get affected by the number of digits?

Suppose I have two 5-digit numbers (A and B) and two 50-digit numbers(C and D). Do the operations A+B and C+D have equal complexity in terms of time and space? or C+D is more complex due to the size of digits?

The complexity of arithmetic operations is typically measured in bit operations, though not everybody agrees this is the correct measure. There is a Wikipedia page listing the complexity of the best algorithms currently known for various operations, including addition and multiplication.

StackExchange Computer Science Q#124158, answer score: 3