A binary digit ( bit ) is a single digit available within the base 2 numbering system.

In base 2 there are only 2 digits. 0 and  1. In contrast there are 10 digits in base 10

(decimal)   0,1,.......9. Since all hardware of computers is such that there are only 2

electrical states (on  /  off), base 2 was chosen as the ideal system for being able to

represent (or show people) what data looked like in the computer. Also for

convenience it was decided to group these bits into clusters of 8 called a byte.

Remember that values ( data ) are what goes into variables. I have already shown you

 the different types of variables but let me simplify it even more by saying that even 

 though there are 8  different types of variables there are only 2 real types of data or

values.  How so ?  If you look closely you will se that a lot of the variable types are

 variations of each other. ( big, small etc ) In  summary then we can say  that all data

 or values fit into one of two general categories :

        NUMERIC                       used in arithmetic

        ALPHANUMERIC          non arithmetic data like addresses

Now I can tell you how data is really stored in memory or on disks.

Alphanumeric data is simple --  there is a unique 16 bit code ( 2 bytes )
                                                       for every possible character that can
                                                       be entered into the computer.

Numeric data is more complicated  -- there is a set number of bytes
                                                                 reserved for each of the various
                                                                 numeric variables and there is not
                                                                 a unique 2 byte code for each digit
                                                                 in the number. All the digits are
                                                                 treated as a unit and stored in
                                                                 arithmetic form using base 2.

The following will explain numeric data representation but only for integers ( whole numbers ) 

1... accept the fact that decimal and binary are positional numbering systems,
       meaning that the true value of the number is derived by multiplying each digit
       by the value of that digit's position and summing the results

2... everyone knows how to count from 0 to 99 in decimal, learn to count from 0 to 99
      in binary. Remember that when the maximum digit is reached in a position you
      start over at zero in that position BUT CARRY just like 5th grade mathematics

        0000   0001   0010   0011   0100   0101   0110   0111  1000   1001   1010

        1011   1100   1101   1110   1111    this was as high as I could go with 4 bits

       I think you see the picture.   NOW imagine you had 16 bits to use.........
       By the way this is the size of a "short integer" variable. Also assume that
       you cannot use the leftmost bit because it is reserved for the sign  1  neg  0 
       pos. That leaves 15 bits and if they were all 1's    0111111111111111   you
       would have a value of 32767 in decimal  or ( 2 to the 16 power ) minus 1.

       Study the above carefully because it is the basis
      for storing numerical values in the computer

       Regular integer variables are 32 bits in size and long integers are 64 bits.
       The principle noted above however is the same for these types.