Page 19 - ComputerScience_Class_11

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

Binary Odometer
Binary odometer is an unusual odometer that 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 then 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 modern computing systems use 16-bit, 32-bit or 64-bit words, which are further divided into 8-bit units. The octal
number system is also used as a short hand for representing file permissions on UNIX systems. 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.

System of Numeration 17