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KEY CONCEPTS
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===Decimal / Binary / Octal / Hexadecimal Numbering Systems===
 
[[Image:decimal-number-3.png|thumb|right|300px|The '''decimal''' numbering system .<br>(Image licensed under [https://creativecommons.org/licenses/by-sa/3.0/ cc] - modified by author).]]
''Decimal Numbers''
 
The '''decimal''' numbering system consists of digits ranging from '''0''' to '''9'''. The numbering system is based on '''sums of the power of 10''' which provides a framework for mathematic calculations.
 
The fact that '''humans''' started counting on their fingers and thumbs most likely lead to the development of this numbering system.
 
Referring to the diagram on the right, the value of each decimal digit consists of the '''value''' (''placeholder'') multiplied by the corresponding power of 10. For example, '''units''' are '''10<sup>0</sup>''', '''tens''' are '''10<sup>1</sup>''', '''hundred''' are '''10<sup>2</sup>''' which move in a '''right-to-left''' direction.
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[[Image:binary-number-3.png|thumb|right|200px|The '''binary''' numbering system.<br>(Image licensed under [https://creativecommons.org/licenses/by-sa/3.0/ cc])]]
''Binary Numbers''
 
The '''binary''' numbering system consists of digits ranging from '''0''' to '''1'''. The numbering system is based on '''sums of the power of 2'''.
 
Digital computers have circuits which representing data in terms of voltage levels. Multiple circuits are used to represent data (in the form of ''binary'' numbers).
 
Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 2. For example, '''2<sup>0</sup>''' , '''2<sup>1</sup>''', '''2<sup>2</sup>''', etc. which move in a '''right-to-left''' direction.
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''Octal / Hexadecimal Numbers''
<table align="right"><tr valign="top"><td>[[Image:octal-number-2.png|thumb|right|200px|The '''octal''' numbering system.<br>(Image licensed under [https://creativecommons.org/licenses/by-sa/3.0/ cc])]]</td><td>[[Image:hex-number-2.png|thumb|right|420px|The '''hexadecimal''' numbering system.<br>(Image licensed under [https://creativecommons.org/licenses/by-sa/3.0/ cc])]]</td></tr></table>
The '''octal''' and '''hexadecimal''' numbering systems consist of digits ranging from '''0 to 7''' and ranging from '''0 to F''' respectively. For ''hexadecimal'' numbers, values for '''10 to 15''' are represented by the characters '''A to F''' respectively. The '''octal''' and '''hexadecimal''' numbering system are based on sums of the power of '''8''' and '''16''' respectively.
 
Since '''1 octal digit represents 3 binary digits''' and '''1 hexadecimal digit represents 4 binary digits''', octal and hexadecimal numbers are used as '''short-cuts''' to represent binary number.
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===Numbering Conversion Methods===
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