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•
The base of the number system (where base is defined as the total number of digits
available in the number system).
4. The number system that we use in our daytoday life is called the decimal number
system. In this system, the base is equal to 10 because there are altogether ten symbols or
digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
5. Some of the positional number systems commonly used in computer design and by
computer professionals are binary (for which base is 2), octal (for which base is 8), and
hexadecimal (for which base is 16).
6. The relationship among decimal, binary, hexadecimal and octal number systems are
given in Figure 3.2.44
I Foundations of Computing
7. Readers must know the techniques for the following types of conversions to convert
numbers from one base to another:
• Converting to decimal from another base
• Converting from decimal to another base
• Converting from a base other than 10 to a base other than 10
• Shortcut method for binary to octal conversion
• Shortcut method for octal to binary conversion
• Shortcut method for binary to hexadecimal conversion
• Shortcut method for hexadecimal to binary conversion
8. Fractional numbers are formed in the same way as in the decimal number system. In
general, a number in a number system with base b would be written as:
anan.1... ao. a.2... a.m
and would be interpreted to mean
an x b" + an., x b""1 + ... + ao x b° + a.! x b"1 + a.2 x b"2 + ... + a.m x b'm
The symbols an, an.i, ..., a.m used in the above representation should be one of the b
symbols allowed in the number system.
Questions
1.
What is the difference between positional and nonpositional number systems? Give
examples of both types of number systems.
2. What is meant by the base of a number system? Give examples to illustrate the role
of base in positional number systems.
3.
What is the value of the base for decimal, hexadecimal, binary and octal number
systems?
4.
Give an example for octal number system to show that the same digit may signify
different values depending on the position it occupies in...
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This document was uploaded on 04/07/2014.
 Spring '14

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