Basic HTML Version

|  | Table of Contents |  | View Full Version

Page 14 - 2606_PlugGPT_C7_Flipbook
P. 14

    Step  2    Add up all the resulting products. This sum gives you the decimal number.

                      Example: Convert (101001)  to decimal number.
                                                  2
                                    4
                            5
                                           3
                                                            1
                                                    2
                      = 1 x 2  + 0 x 2  + 1 x 2  + 0 x 2  + 0 x 2  + 1 x 2 0
                      Sum of the products = 32 + 0 + 8 + 0 + 0 + 1 = 41
                      Therefore, (101001)  = (41) 10
                                          2
                                OPERATIONS ON BINARY NUMBERS

                      We can perform various operations on binary numbers. Let's discuss binary addition and binary
                      subtraction in detail.

                      BINARY ADDITION

                      Binary addition is similar to adding decimal numbers. When the value of addition 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:

                                                   X               Y                  X + Y
                                                   0               0                0 + 0 = 0
                                                   0                1                0 + 1 = 1
                                                   1               0                 1 + 0 = 1

                                                   1                1           1 + 1 = 10 (carry 1)

                      For example, let us add the binary numbers (101111)  and (10111) .
                                                                           2
                                                                                       2
                                                                            ____
                                                          1   1   1  1  1         Carry bits
                                                          1   0  1  1  1  1
                                                      +       1   0  1  1  1
                                                      1   0   0  0  1  1  0

                      BINARY SUBTRACTION
                      In binary subtraction, the smaller binary number is subtracted from the larger one. The table
                      below illustrates how to subtract digit Y from digit X. If Y is greater than X, we borrow 1 from the
                      next higher position. When a binary digit of 0 borrows 1, it effectively becomes 2 (written as 10 in

                      binary). The rules for binary subtraction:
                                               X                  Y                     X – Y

                                               0                  0                   0 – 0 = 0
                                                                                       0 – 1 = 1
                                               0                  1
                                                                             (borrow 1, so that 10 – 1 = 1)
                                                1                 0                    1 – 0 = 1
                                                1                 1                    1 – 1 = 0

                       12   Premium Edition-VII

| 9 10 11 12 13 14 15 16 17 18 19 |