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Hexadecimal

Hexadecimal. Overview. Hexadecimal (hex) ~ base 16 number system Use 0 through 9 and ... A = 10 B = 11 C = 12 D = 13 E = 14 F = 15. Decimal Example. 2657 = 2000 + 600 + 50 + 7 = 2*1000 + 6*100 + 5*10 + 7*1 = 2*10 3 + 6*10 2 + 5*10 1 + 7*10 0. Binary Example.

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Hexadecimal

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  1. Hexadecimal

  2. Overview • Hexadecimal (hex) ~ base 16 number system • Use 0 through 9 and ... A = 10 B = 11 C = 12 D = 13 E = 14 F = 15

  3. Decimal Example 2657 = 2000 + 600 + 50 + 7 = 2*1000 + 6*100 + 5*10 + 7*1 = 2*103 + 6*102 + 5*101 + 7*100

  4. Binary Example 10112 = 1*23 + 0*22 + 1*21 + 1*20 = 1*8 + 0*4 + 1*2 + 1*1 = 8 + 2 + 1 = 1110

  5. Hexadecimal Example A4F16 = 10*162 + 4*161 + 15*160 = 10*256 + 4*16 + 15*1 = 2560 + 64 + 15 = 263910

  6. Hexadecimal  Decimal 6116 = ? F2316 = ? Now convert the above to binary...

  7. Decimal  Hexadecimal • Given the powers of 16: 1, 16, 256, 4096, etc. • Find the power that is just bigger than your number • Go down to the next smallest power of 16 • Divide your number by that power • Round the result down • Make note of the result for that power of 16 • Multiply the rounded down result by its corresponding power of 16…and then subtract that from your original number • Using the result from Step 7, repeat Steps 1-7 until you reach 0

  8. So why do we use hex? • Binary is annoying to read • Hexadecimal is slightly easier • Binary  Hexadecimal is painless • Example: 11101010100101012 = ?

  9. Binary  Hexadecimal • Split the binary number up into 4-bit sections • Determine the hexadecimal value of each section • Bam…you’re done Example: 111010010111010101000101

  10. Hexadecimal  Binary • Determine the 4-bit binary value for each hexadecimal digit • Bam…you’re done

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