Positional notation is basically just a method of representing numbers relevant to their base. In our number system we use base 10. Which means that all numbers are represented by a series of 10 symbols. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) There are many other number bases that can be used and each have their own unique properties that make them useful in different situations. Binary is one such example. Binary is base 2, which means that it uses only 2 symbols to represent all numbers. (0, 1) This is very useful in computers and electronics, which require use of logic gates which have either a on or off, true or false, state.

In our all number systems the base looks the same 10. In base 10 this is simply the number ten. However, in base two or binary 10 represents the number two. We can explore this property by using positional notation. The concept is coupled with the idea of place value. With base ten, we see the number,10, and we know this is basically a ,1, in the tens place and a ,0, in the ones place. To represent this mathematically it will look like: 1 x 10 + 0 x 1 or to look at it relevant to the base it would look like 1 x 10^{1} + 0 x 10^{0.}

The latter is what the number ten looks like in positional notation.

[…] have discussed positional notation in the context of number systems in different bases. However, now taking those concepts a bit […]