Page 14 - TP_Pluse_V2.2_Class_7
P. 14

Example 2: Convert (10111)  to decimal number.
                                             2
                                           3
                                   4
                                                         1
                                                  2
                                    = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 1 × 2 0
                                    = 16 + 0 + 4 + 2 + 1
                                    = 23
                                (10111)  = (23) 10
                                      2
                  Example 3: Convert (101.101)  to decimal number.
                                               2
                       Position         2           1           0                      –1          –2          –3
                     Face value          1          0           1           •           1          0            1
                      Weights           2 2         2 1         2 0                    2 –1        2 –2        2 –3

                                           2
                                                                -1
                                                                        -2
                                                         0
                                                  1
                          101.101 = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 0 × 2  + 1 × 2 -3
                              = 1 × 4 + 0 + 1 × 1 + 1/2 + 0 + 1/8
                              = 4 + 1 + 0.5 + 0.125                Let’s CatCh uP
                              = 5.625                         Convert the binary number 1000.10 into decimal.
                                      (101.101) = (5.625)
                                        2         10











                         OPERATIONS ON BINARY NUMBERS


                  Let's learn the basic operations on binary numbers.

                       Binary Addition

                  Binary addition is similar to the addition of decimal numbers. When the value of sum exceeds the
                  value 1, say 10 or 11, then 1 is carried over to the left of the current position. The rules for adding two
                  binary digits are given below:                              For example,  let  us  add  the  binary

                         X                Y                  X + Y            numbers (101111)  and (10111) .
                                                                                                           2
                                                                                               2
                         0                0                0 + 0 = 0               1   1   1  1  1   _____  Carry bits
                         0                1                 0 + 1 = 1
                          1               0                 1 + 0 = 1              1   0  1  1  1  1
                                                                               +       1   0  1  1  1
                          1               1            1 + 1 = 10 (carry 1)
                                                                               1   0   0  0  1  1  0

                       Binary Subtraction

                  In binary subtraction, binary number of lower value is subtracted from the binary number of higher
                  value. The following table explains the subtraction of digit Y from digit X. If Y is greater than X, then 1
                  is borrowed from the next position. When the binary digit 0 borrows 1 from the next most significant
                  digit, it becomes 10.

                  12    Plus (Ver. 2.2)-VII
   9   10   11   12   13   14   15   16   17   18   19