Find the numbers of codes which can be formed from digits 1 and 0 if they consists 10 digits.

First let's pretend you only have 1 digit, not 10. How many possibilities are there in that case? 0 or 1. That's 2 possible combinations.

How about if you have 2 digits? 00, 01, 10, or 11. That 4 possible combinations.

What about 3 digits? 000, 001, 010, 011, 100, 101, 110, 111. That's 8 combinations.

Do you see the pattern?

The number of combinations is 2 to the power of the number of digits. 1 digit gives you = 2 different possible combinations; 2 digits gives you = 4 different possible combinations; 3 digits gives you = 8 different possible combinations. So 10 digits would give you = 1024 different combinations.