# Changes

## Tutorial4: Data Representation / Numbering Conversion / File Permissions

, 16 January
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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''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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