MGMT 1000 Lecture Notes - Lecture 3: Binary Number
MGMT 1000 Lecture 3 Notes – Numbers as a physical representation
Introduction
• The knowledge of the size limits for calculations in a particular language is sometimes
extremely important
• Since some calculations can cause a numerical result that falls outside the range
provided for the number of bits used.
• In some cases this will produce erroneous results, without warning to the end user of
the program.
• It is useful to understand how the binary number system is used within the computer.
• Often, it is necessary to read numbers in the computer in their binary or equivalent
hexadecimal form.
• For example, colors in Visual Basic can be specified as a six-digit hexadecimal number,
which represents a 24-bit binary number
• Looks informally at number systems in general and explores the relationship between
our commonplace decimal number system and number systems of other bases.
• Our emphasis, of course, is upon base 2, the binary number system.
• The discussion is kept more general, however, since it is also possible, and in fact
common, to represent computer numbers in base 8 (octal) or base 16 (hexadecimal).
• Occasionally we even consider numbers in other bases, just for fun, and also, perhaps,
to emphasize the idea that these techniques are completely general.
• As we embark upon our investigation of number systems, it is important to note that
numbers usually represent some physical meaning.
• For example, the number of dollars in our paycheck or the number of stars in the
universe.
• The different number systems that we use are equivalent.
• The physical objects can be represented equivalently in any of them.
• Of course, it is possible to convert between them.
• For example, there are a number of oranges, a number that you recognize as 5.
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