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Hexadecimal

Learn about the hexadecimal (hex) base-16 number system using 0-9 and A-F, converting between decimal and binary, and the benefits of using hex. Discover how to convert numbers between decimal and hexadecimal, and how to convert binary to hexadecimal and vice versa easily.

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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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