For purely historical reasons, and perhaps due to our # of digits on our hands (that's why they are called digits :-)), we use "base ten". This means that, when we write "10", it is saying "one lot of ten, and zero lots of one" - and one*ten + zero*one = ten!

Imagine we had sixteen digits. Then we might have counted up to sixteen before we had to start grouping things into groups of (not ten but) sixteen.

Then the number "12" would have meant "one lot of sixteen plus two lots of one" and "one times sixteen plus two times one = eighteen".

eighteen divided by six is three.

In base sixteen, we would write this as 12 / 6 = 3

Base sixteen is used a lot in the computer industry, because it is a convenient shorter way of doing base two (binary) arithmetic.

We use the letters A-F to represent the extra "digits", so we count 0 1 2 3 ... 9 A B ... F 10 11 12 13... 19 1A 1B ... 1F

In computer languages, such as C, we need a way of writing these that makes in clear whether you are using base ten or base sixteen. We do this by putting a "0x" on the front to mean hexadecimal - eg



Now, for extra marks, tell me what the \n means! I'll give you a clue, it is ASCII character 0xa.

/Bevin

you lost me at 12 = 18

Consider weights. We can either write "16 ounces" or "1 pound". This doesn't mean 16 = 1, it means that the context the "16" appears in is important.

Consider dates. We write "9/11/2007" and an Australian thinks we are talking about the 9th of November, whereas a New Yorker thinks we are talking about the 11th of September. The exact same characters mean different dates because the two people understand them differently.

Similarly the characters "12" can mean the number twelve to one person, from a society where base 10 is the norm, and the number eighteen to another person from a society where base 16 is the norm.

Very confusing at first - but only because you haven't encountered it before.

Consider the old hymn where "it varies with the wind". The characters "wind" are identical for two different words - the movement of air, and the turning of a coil of spring in an old clock.

So the characters "12" can have many different meanings.

No wonder the poor girl is looking to heaven for guidance.

/Bevin

I sympathize with her. At that age I felt the same way!

When asked my age I may give it in hexadecimal from now on. It sounds better to say I'm 41 (rather than 65). Is that correct? 4x16=64; 64+1=65. Two more months I'll be 42. :)

THANK you, Bevin, for that explanation!

I never learned ANYthing about hexadecimals [or whatever they're called]. This is fascinating.