Binary Numbers

Definition: The Binary system is a very unique system. This system is based on two and the only numbers that you are avalible to use are the numbers 1 and 0. The use of this system is basiclly for computer systems such as the IBC PC. Since the the computer uses two voltage levels (0V for the digit 0 and +5V for the digit 1) the two corrospond between each other using the two digits 1 and 0 and the computers employ the Binary System. It works just like the Decimal System but uses Binary numbers 1 and 0. So basiclly in easier terms the two levels signal eachother for each binary number that is being used. Also if you used any other number other than 1 and 0 the number will be an invalid binary number. And since the Binary System uses  base two here is an example of how the weighted values are:

Also here are some pretty Clear examples of how Binary Numbers look like: 

(The Highlighted numbers on the chart are the actual Binary numbers)

And as many of you know when the United States write there numbers they use commas when they right down there numbers. For Example: 100,000,000 then opposed to 100000000.

With Binary Numbers its the same thing. Except you put a space for every four number. Here is an example for how you write the date in Binary: 1001/1010/11111010111 which is September 10, 2007 in Binary (9/10/07).

Since the Binary Number system is a number system there are Divivding Binary Numbers, Subtracting Binary Numbers, Adding Binary Numbers, and Multiplying Binary Numbers.First here's an example of Dividing Binary Numbers: 

 Here is a link that will tell you more about dividing binary numbers:

Dividing Binary Numbers 

 Now when you multiply binary numbers your doing the same thing as when your muliplying regular numbers, your just using Binary Numbers:

0110 x 10 -----	101 x011 ----	1011 x 11 -----	10 1011 x 1101 --------
11 1011 x10 0110 --------	1010 1001 x 10 0011 ----------	1100 0011 x 101 0001 ----------	1010 0111 x1011 0101 ----------

 starting with a result of 0, shift the second multiplicand to correspond with each 1 in the first multiplicand and add to the result. Shifting each position left is equivalent to multiplying by 2, just as in decimal representation a shift left is equivalent to multiplying by 10.

Here is a link that can tell you more about multiplying binary numbers:

Multiplying Binary Numbers 

 Adding binary numbers is similar to multiplying binary numbers because just like multiplying binary numbers, adding binery numbers is going to be the same as if you were adding regular numbers.

    1
      1011
    +  111
    ------
         0

Now we look at the 2's place. We see 1 + 1 + 1 = 11. So we write a 1 in the 2's place of the answer and carry the 1.

       1 
      1011
    +  111
    ------
        10

We examine the 4's place. 1 + 0 + 1 = 10. Write 0 in the 4's place and carry the 1.

      1  
      1011
    +  111
    ------
       010

The 8's place is next. 1 + 1 = 10. 0 goes in the 8's place, and we carry the 1.

     1  
      1011
    +  111
    ------
      0010

Finally, in the 16's place we have only a 1 to put into the answer.

      1011
    +  111
    ------
     10010

You can see that this is the binary representation of 18, the sum of 11 and 7

Here is a link that can give you more information about adding binary numbers:

Adding Binary Numbers 

And Last but not least there is subtracting binary numbers. When you subtract binary numbers its going to be like as if you were subtracting regular numbers. Just like multiplying and adding the binary numbers. Except their is a twist. When you subtract the numbers you put a 2 after each number to go with each of the rules.

1-18 Now observe the following method of borrowing across more than one column in the example, 1000₂ - 1 ₂: Let’s practice some subtraction by solving the following problems: Q15.Subtract: Q16.Subtract: Q17.Subtract

Here is a link that can give you more information about subtracting binary numbers:

Subtracting Binary Numbers

So to re-fresh your memory, a Binary Numbers are basiclly numbers that consist only of the digits one and two. The reason we use binary numbers is so that computers can operate with all the information that it is delt  with. The way you count by Binary Numbers is starting with the digit one, 1 will equal 0 in binary. Two will equal 1, Three would equal 10, Four would equal 11, Five would equal 100, Six would equal 101, Seven would equal 110, Eight would equal 111, and so on. Remember you can only use the digits one and zero. I hope this information gives you enough information about Binary Numbers.