Powers of Two

You will need to be able to deal with powers of two. In particular, you should have the first eleven of them at your fingertips. This is not hard, but you do need to work at it a little until it becomes automatic. When your memory fails, all you have to do is double the last one you can remember in order to get to the next one. Here are the first eleven:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
The exponents (of 2) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

There is a nice helpful coincidence at the end of this sequence: 2¹⁰ = 1024; the part that will help your memory is that there is a 10 at the beginning of 1024; you can use that to remind yourself that 1024 is 2¹⁰.

Surely you can do the arithmetic in your head up to 128; then there are just two more between there and 1024; if you have to memorize them, do it. After 1024 the arithmetic is still pretty easy for a while: 2048, 4096, 8192, etc. We will use these bigger powers on occasion, so be sure that you can calculate them correctly. After all, multiplying by 2 is pretty easy.