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BINARY NUMBERS

 


First lets look at our decimal number system --we use 10 digits (0 thru 9)

                                                                                                                       

In the number 1247 we have            1 x 1000=1000          Each numbers place tells its value

                                                      +    2 x  100 =  200                     

                                                      +    4 x    10 =    40           We multiply the number times its

                                                      +    7 x      1 =      7           value to get the total value and add

     1247          them together

 

So the value of a decimal number really uses powers of 10 like this

           

            103  102  101  100        Each number (because of its position) tells us

              1     2     4     7          what power of 10 we use to multiply it by.

 

 


The binary number system uses two digits (0 & 1) and it works the same way. 

But binary uses powers of 2!

The position of the digit (0 or 1) tells which value (power of 2) you multiply by.

 

                                                23   22   21   20

So the binary number       1    0    1     1              becomes                   1 x 8 (23) = 8

                                                                                                                        0 x 4 (22) = 0

                                                                                                                        1 x 2 (21) = 2

                                                                                                                        1 x 1 (20) = 1

                                                            and has a decimal value  =                            11

 

 


                                                                                    27   26  25   24  23   22  21  20

so what about the binary number                     1    0    1    1    0    0    1    1

just multiply the value above the digit

by the digit (0 or 1)and add.                     so we have               1 x  128 (27) = 128

                                                                                                            0 x    64  (26)  =   0

                                                                                                            1 x   32  (25)  =  32

                                                                                                            1 x   16  (24)  =  16

                                                                                                            0 x     8  (23)  =    0

                                                                                                            0 x     4  (22)  =    0

                                                                                                            1  x    2  (21)  =    2

                                                                                                            1  x    1  (20)  =    1

                                                                        decimal value  =                                 179

 

 


How about the binary number                            1   0   0   0   0   0   0   1

 

Don’t add the 0 positions— just the places where there is a 1, right?

 


Now try the binary number                                  0   0   0   1   1   1   1   1

Notice that if you start on the right hand

end, the place value doubles moving left

128    64    32    16    8    4    2    1

just add them up!