1What is the last digit of even numbers in binary, and what is it for odd numbers?
Even and odd numbers differ in their last binary digit: if the last digit is 0, the number is even; if the last digit is 1, the number is odd.
2What do the powers of 2 (2⁰, 2¹, 2², 2³ and 2⁴) look like in binary?
In binary, powers of 2 have a very simple form. Every power of 2, say 2n in decimal, looks like a 1 followed by n zeros in binary.
3What can you conclude? How can we write any natural number?
Every natural number can be written as a sum of powers of 2. The 1s in the binary form show which powers we add.