Decimal to-hexadecimal

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Learn to convert decimal numbers to hexadecimal ones, and hexadecimal numbers back to decimal system. This base conversion has to do with programming and digital electronics.

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Decimal to-hexadecimal

  1. 1. Decimal to Hexadecimal and Hexadecimal to Decimal 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. System Numbers <ul><li>Binary Octal Decimal Hexadecimal </li></ul><ul><li>0 - 1 0 - 7 0 - 9 0 – 9 and </li></ul><ul><li> A = 10 </li></ul><ul><li> B = 11 </li></ul><ul><li> C = 12 </li></ul><ul><li> D = 13 </li></ul><ul><li> E = 14 </li></ul><ul><li> F = 15 </li></ul>
  4. 4. <ul><li>A7F4 H = A x 16 3 10 x 16 3 </li></ul><ul><li>7 x 16 2 7 x 16 2 </li></ul><ul><li>F x 16 1 15 x 16 1 </li></ul><ul><li>4 x 16 0 4 x 16 0 </li></ul><ul><li> 42,996 10 </li></ul>Hexadecimal Numbers to Decimal 3 2 1 0 power of 16
  5. 5. <ul><li>0.1A2 16 = 1 x 16 -1 0.0625 </li></ul><ul><li>10 x 16 -2 0.0390625 </li></ul><ul><li>2 x 16 -3 0.00048828 </li></ul><ul><li> 0.10205078 10 </li></ul>Hex Numbers to Decimal 0 -1 -2 -3 power of 16
  6. 6. Decimal to Hexadecimal <ul><li>3168 10 = ? 16 </li></ul><ul><li>3168 / 16 = 198 and rem = 0 ( _ _ _ 0 16 ) </li></ul><ul><li>198 / 16 = 12 and rem = 6 ( finish! C60 16 ) </li></ul><ul><li>(keep dividing by the base until quotient < base) </li></ul>
  7. 7. Decimal to Hexadecimal <ul><li>7732 10 = ? 16 </li></ul><ul><li>7732 / 16 = 483 and rem = 4 ( _ _ _ 4 16 ) </li></ul><ul><li>483 / 16 = 30 and rem = 3 ( _ _ 34 16 ) </li></ul><ul><li>30 / 16 = 1 and rem = 14 ( finish! 1E34 16 ) </li></ul><ul><li>(keep dividing by the base until quotient < base) </li></ul>
  8. 8. Decimal Numbers to Hex <ul><li>0.342 10 = ? 16 </li></ul><ul><li>0.342 x 16 = 5 .472 ( . 5 16 ) </li></ul><ul><li>0.472 x 16 = 7 .552 ( . 57 16 ) </li></ul><ul><li>0.552 x 16 = 8 .832 ( . 578 16 ) </li></ul><ul><li>0.832 x 16 = 13 .312 ( . 578D 16 ) </li></ul><ul><li>0.342 10 ≈ 0.578D 16 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>
  9. 9. 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>
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