Binary

From category: Miscellaneous

As some of you may realise, computers (and electronics in general) don't understand words. They can only understand numbers. And, for the moment, computers work on the principle of on/off switches. (Actually, it's on the principle of voltages above and below certain thresholds, but I digress)

Anyway, computers use a system known as binary (base 2, prefix bi- from Greek) to make sense of their numbers, and inside a computer everything is stored as numbers. The most common representation of numbers to letters (which affects most things) is called ASCII, the American Standard Code for Information Interchange. Computers since the late 1970s (may even be earlier) have used this.

In ASCII, for example, the capital letter A is code 65. Z is 90. a is 97. Each letter has its own unique number. The digits 0-9, plus all the punctuation and symbols all have their own numbers as well.

So what about binary? Well, computers store all this information in long strings of 0s and 1s, as binary only has these two digits. How do we get to 90, then, if we only have 2 different digits? Well...

In decimal (base 10), we consider a number like 4,096 like so:

 th  hu  tn  un
  4   0   9   6

The columns mean, respectively, thousands, hundreds, tens and units (just like we were taught in school!). So the number 4,096 means 4 lots of 1,000, no 100s, 9 lots of 10 and 6 lots of 1. More simply:

 4 x 1000 + 0 x 100 + 9 x 10 + 6 x 1

What happens is that when we run out of space in one column (like when we get past 9 in the units, we have to go to 10), we make another column one order higher. Binary does the same but instead of columns going in 10s, they go in 2s. So, 1, 2, 4, 8, 16, 32, 64 and so on.

It will hopefully be easier to understand when we use an example. Let's start off with 65, for A, like we had earlier.

 128  64  32  16   8   4   2   1
   0   1   0   0   0   0   0   1

From that, we can see that 65 = 1x64 + 1x1, and this gives us the numbering of 01000001 for 65. We typically group them in blocks of 8, just to keep life a little simpler (it is only too likely to have errors if trying to type in blocks of more than about 10 anyway, and 8 is a good choice, as it is part of the order anyway)

The translator on this site pulls out each character supplied and returns the equivalent 8-digit (called bit) represntation for each letter, number, symbol or whatever.

This voice is available for text manipulation only, not for the full webpage translation treatment. We are looking into whether can expand this voice to include the full webpage treatment, but it might not be possible.