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The Essence of

Binary & Hexadecimal


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This is only here for those who really feel
they want to know more on the subject!!

Because of having ten fingers and ten toes (usually!), the figure 10 has become important as a base unit for arithmetic. So, when we count up from 1 to 10, we reach 9 and then put a "1" to the left and a nought to the right to signify arriving at 10, and starting a new column for the next series up to 9. The old "tens" and "units". When we get to 99, we again add a nought to the right to give us 100 ---- and so on.

Simple eh? Well - computers, thus far at least, work on the principle of just two states existing - either a "0" or a "1" (an "on" or an "off" state if you like, in switching terms, or "true" and "false"). In order to make this useful, a method of deriving many numeric values from just these two states was implemented, called "Binary".


Quite simply, this is arithmetic to a base 2 instead of 10. So, we count from "0" to "1" and then we go back to "0"and carry "1" into a new column to the left. If we use just a four digit series of binary as an example, it should be possible to see how this works...........

0000 in binary is of course, in decimal, just zero. 0001 in binary equates to decimal "1". Then we have 0010 in binary (0 + 0 + 2 + 0), which is a decimal "2". 0011 binary (0 + 0 + 2 + 1) is decimal "3".......and so on. When we reach binary 1111, this is the same as a decimal value "15" (8 + 4 + 2 + 1) - see how the base 2 is incrementing?

This so far has looked at just "4 bit" binary (4 bits is sometimes called a "nibble", or used to be anyway!). If we go to "8 bit" binary, then the total value possible in decimal is 255, (128 + 64 + 32 + 16 + 8 + 4 + 2 + 1), but
including a zero, we have 256 "states" - and this 255 looks like - 11111111. This set of eight bits is, by the way known as a "byte". Notice how we have the "magic 255" total now, which you can relate to the color information you may have read - the "8 bit" color, with 256 states (including zero).


Right - enough of binary - you'll just have to find some books to go into this in detail if you want - same for hex' - we are after all simply touching on the subject. Hexadecimal is really just a very compact from of binary and makes for a much tidier way of writing it.

Instead of masses of "0's" and "1's" we now work to a base 16 and so compact our information. Remember how a binary 4 bit string is 1111 (8 + 4 + 2 + 1) = 15. Well, if we call this "F" - (necessary because to get to 15 with only one character) - we have to "extend" our decimal number series such that we go, 1................8,9,A,B,C,D,E & F. Wierd eh? But it works well.

So, we can now show 15 decimal (or 1111 binary) as "F" in hexadecimal. After we reach "F" we have to "carry" as usual to continue, but, because we are on base 16, we go as follows - 15 decimal, as said, is "F" in hex' - but to get to 16, we "carry" the "F" one place left and put in a "1" instead, which signifies a value of 16, and then a "nought" goes on the right. Thus, 16 decimal becomes "10" in hex' (usually shown as 10H). Got it? - (16 + 0) = 16. Lets show another example or two........

What would 27 be in hex'? - well 16 into that goes once and so gives a "1" on the left, leaving remainder 11 on the right ("units"). 11 in hex is "B". So, 27 decimal in hex' becomes "1B" (1BH) (16 + 11) = 27.

"FF" of course is ((16 x 15) + 15) = 255 - again, we have the magic number, zero being the other state to give a total of 256. Thus now we can express a "byte" value as just two characters - very economical.

Try this - what is "D9" hex', in decimal terms? Well, multiply the left hand element by 16 - this is therefore (D x 16) = (13 x 16) = 208. To this we add the "units" element on the right, which is 9, thus giving (208 + 9) = 217 decimal.

Finally, working the other way from decimal to hex' - what is 98 in hex'? Well, this time, divide the figure by 16 - this gives a result of 6 with 2 over ((6x16) + 2), and so our hex' equivalent is 62H.

Exhausted? - probably! This is only however the briefest of introductions and is covered at all just because we have discussed the colors aspect of web design. If you're more confused than before, then apologies - it is after all just a surface scratcher and not really too important unless you are interested! Nevertheless, it may now just be possible to appreciate what color values might be, whether shown in RGB decimal, or RGB hex' notation.

A full blown red, would be shown as either 255,0,0 in decimal, or #FF0000 hex'. 0,153,51 decimal is #009933 in hex', and this is a web-safe lightish green - notice the increments referred to in the description on the "colors" page. Now - you may go and rest and treat yourself to a drink!

OK - it's boring, perhaps!! I do find though that from time to time, people ask about this.... if only because of a wish to better understand some of the basics of computers, and the deeper aspects of digital imaging and processing.

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