Number Systems Conversion PDF
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Uploaded by WonderfulDanburite
Faculty of Science
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This document explains various number systems, including decimal, binary, octal, and hexadecimal. It provides examples of conversions between these systems, including decimal to binary, octal to binary, binary to hexadecimal, and detailed explanations for each conversion.
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# Number Systems ## Decimal System - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ## Binary System - 0, 1 ## Octal System - 0, 1, 2, 3, 4, 5, 6, 7 ## System XVI - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 - A, B, C, D, E, F ### Converting from Decimal to Binary **Example 1:** - ( 0.10)<sub>10</sub>...
# Number Systems ## Decimal System - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ## Binary System - 0, 1 ## Octal System - 0, 1, 2, 3, 4, 5, 6, 7 ## System XVI - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 - A, B, C, D, E, F ### Converting from Decimal to Binary **Example 1:** - ( 0.10)<sub>10</sub> → ( 0.5)<sub>10</sub> - (0 + 4 + 0 + 1)<sub>10</sub> **Example 2:** - (367)<sub>8</sub> → (247)<sub>10</sub> - (3 * 8<sup>2</sup> + 6 * 8<sup>1</sup> + 7 * 8<sup>0</sup>)<sub>10</sub> **Example 3:** - (7E14)<sub>16</sub> → (126)<sub>10</sub> - (7 * 16<sup>2</sup> + E*16<sup>1</sup> + 14 *16<sup>0</sup>)<sub>10</sub> **Example 4:** - (36)<sub>10</sub> → (200)<sub>8</sub> | Decimal | Octal | |---|---| | 36 | 2 | | 18 | 0 | | 9 | 0 | | 4 | 2 | | 2 | 0 | | 1 | 1 | | 0 | 0 | ### Converting from Octal to Binary **Example 1:** - (554)<sub>8</sub> → ( 101 101100)<sub>2</sub> - ( 5 * 8<sup>2</sup> + 5 * 8<sup>1</sup> + 4 * 8<sup>0</sup>)<sub>8</sub> - ( 1 * 2<sup>7</sup> + 0 * 2<sup>6</sup> + 1 * 2<sup>5</sup> + 1 * 2<sup>4</sup> + 1 * 2<sup>3</sup> + 0 * 2<sup>2</sup> + 1 * 2<sup>1</sup> + 0 * 2<sup>0</sup>)<sub>2</sub> **Example 2:** - ( 554)<sub>8</sub> → ( 101 101100 )<sub>2</sub> - (0001011012200)<sub>2</sub> ### Converting from Binary to Octal **Example 1:** - (101101100)<sub>2</sub> → (554)<sub>8</sub> - (1 * 2<sup>7</sup> + 0 * 2<sup>6</sup> + 1 * 2<sup>5</sup> + 1 * 2<sup>4</sup> + 1 * 2<sup>3</sup> + 0 * 2<sup>2</sup> + 1 * 2<sup>1</sup> + 0 * 2<sup>0</sup>)<sub>2</sub> - ( 4 + 0 + 2) * 8<sup>2</sup> + ( 4 + 0 + 2 ) * 8<sup>1</sup> + ( 4+ 0 + 0) * 8<sup>0</sup> )<sub>8</sub> - (5 * 8<sup>2</sup> + 5 * 8<sup>1</sup> + 4 * 8<sup>0</sup>)<sub>8</sub> ### Converting from Binary to Hexadecimal **Example 1:** - (000201102100)<sub>2</sub> → (12C)<sub>16</sub> - (0001 * 2<sup>11</sup> + 0 * 2<sup>10</sup> + 1 * 2<sup>9</sup> + 1 * 2<sup>8</sup> + 0 * 2<sup>7</sup> + 2 * 2<sup>6</sup> + 1 * 2<sup>5</sup> + 0 * 2<sup>4</sup> + 2 * 2<sup>3</sup> + 1 * 2<sup>2</sup> + 0 * 2<sup>1</sup> + 0 * 2<sup>0</sup>)<sub>2</sub> - (0 + 4 + 2) * 16<sup>1</sup>+ ( 8 + 4 + 0) * 16<sup>0</sup>)<sub>16</sub> - ( 6 * 16<sup>1</sup> + 12 * 16<sup>0</sup>)<sub>16</sub> - (12C)<sub>16</sub>
