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    OCTAL NUMBER SYSTEM

                      The octal number system consists of eight digits from 0 to 7. Hence, the base of octal number
                      system is 8. In this system, the position of each digit represents a power of 8. For example, (345)₈
                      is an octal number. Octal makes long binary numbers shorter and simpler. The place value of
                      digits according to the position and weight is as follows:

                                     Position       2          1         0                   –1        –2
                                                                                   •
                                      Weight        8 2       8 1       8 0                 8 –1      8 –2

                            HEXADECIMAL NUMBER SYSTEM

                      The hexadecimal number system consists of 16 digits from 0 to 9 and A to F. The letters A to F
                      represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position
                      in hexadecimal number system represents a power of 16. For example, the number (764)  is a
                                                                                                                    16
                      hexadecimal number. The place value of the digits according to position and weight is as follows:

                                     Position       2          1         0                   –1        –2
                                                                                   •
                                      Weight       16 2       16 1      16 0                16 –1     16 –2

                            COMPUTER ARITHMETIC

                      Let's learn the basic computer arithmetic on binary numbers.

                      Binary Addition

                      Binary addition is similar to the addition of decimal numbers. In Binary Number System, 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

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