why and how binary system is used to represent data in a computer system?

Answer 1

basically computers contain millions (trillions even) of switches

A switch can be either on or off (represented by 1 or 0 in binary)

1 byte is equal to 8 of these switches (bits) and is capable of storing any number between 0 (00000000) and 255 (11111111)

so your 40 Gb hard drive actually contains over 320,000,000,000 bits that are switched to either 1 or 0

Answer 2

The binary number system is a base two system. It's like this:

In a base ten system (the one we always use every day), you count things up to nine and then when you reach the next one, you begin a new column and set the column on the right back to zero again.

You're saying "Huh? What're you blabbering about?" The number ten has two digits, a one and a zero. When you begin counting from one, you count up to nine. The next thing you count will make ten. You will be finished with using a single column and begin a new column for groups of ten. The number ten ("10") means one group of ten and no extra past ten ("one-zero").

Now, in a base two system, instead of counting up to nine and creating a second column for the tenth thing you count, you create a second column for the SECOND thing you count. So it goes like this:

1
10
11
110
111
1110
1111
11110
and so on....

The reason computers are designed to use this type of system is because computer comands in a program are broken down into two possible results; "if x then y, if not x then z".

Hope this helps you.