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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.

For example,

(7592)

10

is of base 10 number system.

(214)

8

is of base 8 number system.

(123)

16

is of base 16 number system.

Number Systems

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