When a number is written in "binary" everything is a power of two. The binary number 101101 **means**** \(\displaystyle 1\times 2^5+ 0\times 2^4+ 1\times 2^3+ 1 \times 2^2+ 0\times 2^1+ 1\times 2^0= 1\times 32+ 0\times 16+ 1\times 8+ 1\times 4+ 0\times 2+ 1\times 1= 32+ 8+ 4+ 1= 45 base 10.**

Each of the "bits", one binary unit, is either "0" or "1". It is easier for a computer to store numbers in "binary" because we can each "bit" can be stored as a switch "on" for 1 or "off" for 0. We **could** store numbers in base 10 but then we would need to distinguish between 10 different levels of current in a switch- and that leads to difficulties distinguishing between slightly different levels.

As I said, a single "bit" is either 0 or 1. Because it is easier for a computer to work in "binary" it is also easier to have registers with a power or two number of bits. 8 bits is called a "byte" and can store \(\displaystyle 2^9= 256\) distinct numbers. Most registers in modern computers are either a "byte" or a "word"- two bytes so 16 bit which can store \(\displaystyle 2^{16}= 65536\) distinct numbers.

While for "normal people", "K" represents 1000 (kilo as in kilogram, 1000 grams, or kilometer, 1000 meters) for computer folk, who just love to work with powers of 2, "K" is \(\displaystyle 2^{10}= 1024\) (the power of 2 closest to 1000). "Giga" is the prefix for \(\displaystyle 10^9\) which is 1 million "K". \(\displaystyle 2^{30}= 1073741824\) is the power of 2 closest to that.\)