Page 17 - computer science (868) class 11
P. 17

Say any binary number 100111.0101 can be represented as,

                               2 5    2 4     2 3    2 2     2 1    2 0           2 -1    2 -2   2 -3    2 -4
                               1       0      0       1      1      1       .      0      1       0      1

                 The leftmost bit contains maximum weight and is called the Most Significant Bit or MSB. The rightmost bit contains
                 minimum weight and is called the Least Significant Bit or LSB.

                 Binary Odometer
                 Binary odometer is an unusual odometer which is initialised to 0000. When each wheel turns, the value changes
                 from 0 to 1. With another turn it changes back to 0 because each wheel has only two digits 0 and 1. After completing
                 1 km, the odometer reads 0001. After travelling 2 km, the rightmost tab is reset to 0 and its previous tab changes to 1.
                 Similarly, on covering 3 km, the odometer reads 0011 and on completing 4 km, the previous left tab is set to 1 and the
                 right tabs are reset to 0. It reads 0100. The process continues as is demonstrated in the table below. The binary value
                 of decimal numbers from 0 to 15 are as follows:

                            Decimal Number                            Binary Equivalent
                                  0                0                0                0                0
                                  1                0                0                0                1

                                  2                0                0                1                0
                                  3                0                0                1                1
                                  4                0                1                0                0
                                  5                0                1                0                1
                                  6                0                1                1                0

                                  7                0                1                1                1
                                  8                1                0                0                0
                                  9                1                0                0                1
                                  10               1                0                1                0
                                  11               1                0                1                1

                                  12               1                1                0                0
                                  13               1                1                0                1
                                  14               1                1                1                0
                                  15               1                1                1                1

                 1.1.3 Octal Number System
                 All the modern generation computing systems use 16-bit, 32-bit or 64-bit words which are further divided into 8-bit
                 words based on the Octal number system. The octal number system is also used as a short-hand for representing file
                 permissions on UNIX systems and UTF-8 numbers. Transponders used in aviation industry transmit octal codes.


                                                               Definition

                      Octal number system has base 8. The available digits are 0, 1, 2, 3, 4, 5, 6, 7. Like previous number systems, it is also
                      a positional value-based system where each digit has its weight denoted as a power of 8.








                                                                                                                        15
                                                                                                            Numbers     15
   12   13   14   15   16   17   18   19   20   21   22