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l'Ktonos
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Reading and Writing in Binary Code
« Thread Started on Nov 18, 2003, 3:15pm »

Reading and Writing in Binary Code

Numbers
In order to understand binary numbers, you need to understand how binary interprets numbers. They typical binary number code consists of eight numbers, made up of ones (1) and zeros (0). The default binary number would be zero, which looks like this:

00000000

Each 0 is a placeholder, exactly like the 1s, 10s, 100s, 1000s, etc in the normal numbers we’re used to using. The difference is that after you change a 0 to a 1, you don’t look at the value as it appears (00000010 = 2, not 10). What you must see is that each time you change a 0 to a 1, you change the value of the placeholder by a certain amount, then you must add all the values that the 1’s represent together for the true number (you should always remember that the value can never be higher than 255, for reasons I will later explain). The values are found by doubling the number that came just before it, as shown here:

..0...0...0..0..0.0.0.0
128 64 32 16 8 4 2 1

The first placeholder is 1 and starts on the right. Double that to get 2, then 4, then 8, then 16 and on and on until you get to 128 in the eighth placeholder (on the far left). Looking at this, you can understand why the highest number in binary can be 255. If my code looked like this…

11111111

…I would be adding 1+2+4+8+16+32+64+128 which equals 255. The trick to getting any number you want is simple addition. You have to come up with the right combinations of 1’s and 0’s for the number you want. Take, for example, the number 43. The first thing you should notice is that it’s an odd number, meaning you’ll need a 1 in the first placeholder:

00000001

The next thing you must do is find the value (128, 64, 32, 16, 8, 4, 2, or 1) that comes closest to 43 without exceeding it. Change that placeholder to a 1. For 43, that would be 32 (the 6th placeholder), so now you have:

00100001

Now your total value has climbed to 33, meaning we need to add 10 to get 43. Follow the same step as before, changing the placeholder whose value comes closest to the number that you need, without exceeding it. In this case it would 8, the 4th placeholder. Which gives you:

00101001

Your total value is now 41, leaving you with only having to add 2 to it to equal 43. Following the same step as before (or just using common sense), you can deduct that the 2nd placeholder is the one you’ll need to change to 1 in order to reach the wanted number. That leaves you with:

00101011

Add up the values that each 1 stands for, and you’ll get 32+8+2+1=43. Simple as that. Now if you think you understand how the number system works, try some problems and pm me your results…

Change the normal numbers to binary code:
143
25
68
206
180

Change the binary code into normal numbers:
01010011
00001110
01001011

Letters
I could give you a list of the alphabet with it’s binary equivalent next to it, allowing you to simply copy and paste them into words, but then you would never understand the pattern of how binary letters work. So instead I’ll tell you this pattern, and allow you to figure the letters out yourselves.

Every binary letter consists of eight numbers, each number being either a one (1) or a zero (0). Starting from the left, the second two numbers are used for deciding whether the letter is an uppercase or lowercase letter (the number on the far left will always be 0). An uppercase letter is always defined by a 10 in the second two number slots, and a lowercase number is defined by a 11 in those spots.

For convenience, let’s look at the binary letters 01000001(A) and 01100001(a). The first letter is uppercase (note the 010) whereas the second one is lowercase (note the 011). If you’re looking to really learn binary writing, that should be the first thing you notice.

Next we’ll move on to the pattern of how to recognize different letters. The letter is defined by the last five numbers, starting from the right of the two used to define the case. The key is to understand how numbers are shown in binary code, because each letter is defined by its number place in the alphabet (A=1, B=2, C=3) using the binary number code system. Since you’ve already covered that, finding out a number between 1 and 26 should be no problem. The trick to the letter system, is that you use only the five placeholders on the right:

00000000

The highest number you’ll need is 16, the fifth placeholder, and using combinations of the other placeholders, you can come up with any number between 1 and 26.

Now see if you can list the entire alphabet (both cases) using binary code and pm me your results. Remember the system:

000 + 00000
Uppercase or Lowercase + What number in the alphabet?

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