1. Define number system. Write in brief about positional and non-positional number system.
Ans: A number system defines a set of values used to represent ‘quantity’. In ancient times, people
used to count on their fingers. When the fingers became insufficient for counting, stones, pebbles or
sticks were used to indicate the values. This method of counting is called the ‘non-positional number
system’. It was very difficult to perform arithmetic with such a number system, as it had no symbol for
zero. The most common non-positional number system is the Roman number system, in which only a
few characters such as I, V, X, L, C, D and M are used to represent the numbers. These systems are often
clumsy and it is very difficult to perform calculations for large numbers.
On the other hand, a ‘positional number system’ requires a finite number of symbols/digits of the sys-
tem to represent arbitrarily large numbers. When using these systems, the execution of numerical calcu-
lations becomes simplified because a finite set of digits are used. The value of each digit in a number is
defined not only by the symbol, but also by the symbol’s position. The most popular positional number
system being used today is the decimal number system. Some other commonly used positional number
systems include binary, octal and hexadecimal number systems.
2. What information is conveyed by radix in the number system? Tabulate the types of
number systems used by the computers.
Ans: In the number system, the ‘radix’ (also called ‘base’) tells the number of symbols used in the
system. In the earlier days, different civilizations were using different radixes. The Egyptians used the
radix 2, the Babylonians used the radix 60 and Mayans used the radixes 18 and 20. In contrast, modern
computers use the radix 2 because they recognize only two symbols, which are represented in digital
circuits as 0s and 1s. The radix of the system is always expressed in decimal numbers. The base or radix
of the decimal system is 10. This implies that there are 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Similarly,
the system using three symbols 0, 1 and 2 will be of base 3; four symbols will be of base 4 and so forth.
The base of a number system is indicated by a subscript (decimal number) and this will be followed
by the value of the number.
is of base 10 number system.
is of base 8 number system.
is of base 16 number system.
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