Binary Number System


Most modern computer systems operate using binary numbers.With two levels we can represent exactly two different values.These could be any two different values,and those two values are zero and one( 1 and 0).

The decimal number system that people use every day contains ten digits, 0 through 9. Start counting in decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, oops! There are no more digits left. How do we continue counting with only ten digits? We add a second column of digits, worth ten times the value of the first column. Start counting again: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 (Note that the right column goes back to zero here.), 21, 22, 23, ... , 94, 95, 96, 97, 98, 99, oops! Once again, there are no more digits left. The only way to continue counting is to add yet another column worth ten times as much as the one before. Continue counting: 100, 101, 102, ... 997, 998, 999, 1000, 1001, 1002, .... You should get the picture at this point.
Another way to make this clear is to write DECIMAL numbers in expanded notation 1032 is equal to 1 1 000's +0 100's +3 10's +2 1's . By writing numbers in this form, the value of each column becomes clear.
The binary number system works in the exact same way as the decimal system, except that it contains only two digits, 0 and 1. Start counting in binary: 0, 1, Oops! There are no more binary digits. In order to keep counting, we need to add a second column worth twice the value of the column before. We continue counting again: 10, 11, oops! It is time to add another column again. Counting further: 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111.... Watch the pattern of 1's and 0's. You will see that binary works the same way decimal does, but with fewer digits.
Binary uses two digits, so each column is worth twice the one before. This fact, coupled with expanded notation, can be used convert between from binary to decimal. In the binary system, the columns are worth 1, 2, 4, 8, 16, 32, 64, 128, 256, etc. To convert a number from binary to decimal, simply write it in expanded notation. For example, the binary number 101101 can be rewritten in expanded notation as 1. By simplifying this expression, you can see that the binary number 101101 is equal to the decimal number 45.

An easy way to convert back and forth from binary to decimal is to use Microsoft Windows Calculator. You can find this program in the Accessories menu of your Start Menu. To perform the conversion, you must first place the calculator in scientific mode by clicking on the View menu and selecting Scientific mode. Then, enter the decimal number you want to convert and click on the Bin check box to convert it into binary. To convert numbers from binary to decimal, click on the Bin check box to put the calculator in binary mode, enter the number, and click the DEC check box to put the calculator back in decimal mode.


HERE IS SOME LINKS THAT HELPS YOU TO KNOW MORE ABOUT BINARY NUMBERS:
http://www.usbyte.com/common/binarysystem.htm
http://l3d.cs.colorado.edu/courses/CSCI1200-96/binary.html