Questions I need to answer for a test review

Question

1. What does it mean to:
2. Rewrite a number to a different base
3. Add two or three numbers to a different base
4. Subtract two numbers in a different base
5. Why do we learn to work with numbers in different bases?

Answer 1

15 = 2^3+2^2+2^1 +2^0 or 15 base 10 = 1111 base 2

43 = 3^3 + 3^3+2*3^1+3^0 or 43 base 10 = 1121 base 3 etc

Answer 2

There are tricks for doing conversion between bases.

I cannot easily review those tricks with you here.

There are 2 important reasons for learning about numbers in other bases.

Binary, Octal and Hexadecimal, i.e. base 2, base 8 and base 16, numbers are useful in understanding how computers work.

Understanding numbers in other bases should give a better understanding of what base 10 numbers mean.