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# Binary to-decimal

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Learn to convert binary numbers to decimal ones, and decimal numbers to binary. These concepts are used mainly in programming or digital electronics.

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### Binary to-decimal

1. 1. Binary to Decimal and Decimal to Binary Base Conversion
2. 2. <ul><li>2,345 10 = 2000 2 x 10 3 </li></ul><ul><li> 300 3 x 10 2 </li></ul><ul><li> 40 4 x 10 1 </li></ul><ul><li> 5 5 x 10 0 </li></ul>Decimal Numbers 3 2 1 0 power of 10
3. 3. <ul><li>1011 2 = 1 x 2 3 8 </li></ul><ul><li>0 x 2 2 0 </li></ul><ul><li>1 x 2 1 2 </li></ul><ul><li>1 x 2 0 1 </li></ul><ul><li>11 10 </li></ul>Binary Numbers to Decimal 3 2 1 0 power of 2
4. 4. <ul><li>0.1011 2 = 1 x 2 -1 0.5 </li></ul><ul><li>0 x 2 -2 0 </li></ul><ul><li>1 x 2 -3 0.125 </li></ul><ul><li>1 x 2 -4 0.0625 </li></ul><ul><li> 0.6875 10 </li></ul>Binary Numbers to Decimal 0 -1 -2 -3 -4 power of 2
5. 5. Decimal Numbers to Binary <ul><li>18 10 = ? 2 </li></ul><ul><li>18 / 2 = 9 and rem = 0 ( _ _ _ _ 0 2 ) </li></ul><ul><li>9 / 2 = 4 and rem = 1 ( _ _ _ 10 2 ) </li></ul><ul><li>4 / 2 = 2 and rem = 0 ( _ _ 010 2 ) </li></ul><ul><li>2 / 2 = 1 and rem = 0 ( finish! 10010 2 ) </li></ul><ul><li>(keep dividing by the base until quotient < base) </li></ul>
6. 6. Decimal Numbers to Binary <ul><li>23 10 = ? 2 </li></ul><ul><li>23 / 2 = 11 and rem = 1 ( _ _ _ _ 1 2 ) </li></ul><ul><li>11 / 2 = 5 and rem = 1 ( _ _ _ 11 2 ) </li></ul><ul><li>5 / 2 = 2 and rem = 1 ( _ _ 111 2 ) </li></ul><ul><li>2 / 2 = 1 and rem = 0 ( finish! 10111 2 ) </li></ul><ul><li>(keep dividing by the base until quotient < base) </li></ul>
7. 7. Decimal Numbers to Binary <ul><li>0.342 10 = ? 2 </li></ul><ul><li>0.342 x 2 = 0 .684 ( . 0 2 ) </li></ul><ul><li>0.684 x 2 = 1 .368 ( . 01 2 ) </li></ul><ul><li>0.368 x 2 = 0 .736 ( . 010 2 ) </li></ul><ul><li>0.736 x 2 = 1 .472 ( . 0101 2 ) </li></ul><ul><li>0.342 10 ≈ 0.0101 2 it’s an approximation </li></ul><ul><li>Take the integer part of every multiplication to form the binary number. You can go on many more multiplications to improve the accuracy of the conversion </li></ul>
8. 8. Online Base Conversion <ul><li>For an online calculator for base conversions, see: </li></ul><ul><li>matrixlab - examples.com /base- conversion.html </li></ul>