Hexadecimal numbers

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Hexadecimal numbers

  1. 1. An Introduction to Computer Hardware - BKHS Hexadecimal Numbers 1 01/08/14
  2. 2. Introduction to Hexadecimal • Base-16 number system •16 Unique symbols •Numbers 0 to 9 and letters A to F •Decimal 10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F •Can represent every byte (8 bits) as two hexadecimal digits •Easier for humans to read hexadecimal rather than binary •Hexadecimal numbers usually have either an 0x prefix or an h suffix. Example: 0x3F7A, 85D2h 2 01/08/14
  3. 3. Converting Decimal to Hex 1. Divide the decimal number by 16. Treat the division as an integer division. 2. Write down the remainder (in hexadecimal). 3. Divide the result again by 16. Treat the division as an integer division. 4. Repeat step 2 and 3 until result is 0. 5. The hex value is the digit sequence of the remainders from the last to first. 3 01/08/14
  4. 4. Decimal to Hex Example Convert 837 to Hex 837/16 = 52 r 5 Least significant 52/16 = 3 r 4 3/16 = 0 r 3 Most Significant 0x345 or 345h 4 01/08/14
  5. 5. Converting Hex to Decimal 1. 2. 3. 4. 5. 6. 7. Get the last digit (LSD) of the hex number, call this digit the currentDigit. Make a variable, let's call it power. Set the value to 0. Multiply the current digit with (16^power), store the result. Increment power by 1. Set the the currentDigit to the previous digit of the hex number. Repeat from step 3 until all digits have been multiplied. Sum the result of step 3 to get the answer number 5 01/08/14
  6. 6. Hex to Decimal Example Convert 0x58B to Decimal Last digit (LSD) = 0xB = 11(decimal) 16^0 = 1, 1 x 11 = 11 Next digit = 8 16^1 = 16, 8 x 16 = 128 Next digit (MSD) = 5 16^2 = 256, 5 x 256 = 1280 1280 + 128 + 11 = 1409 decimal 6 01/08/14
  7. 7. Hex to Decimal Example Convert 0x58B to Decimal Last digit (LSD) = 0xB = 11(decimal) 16^0 = 1, 1 x 11 = 11 Next digit = 8 16^1 = 16, 8 x 16 = 128 Next digit (MSD) = 5 16^2 = 256, 5 x 256 = 1280 1280 + 128 + 11 = 1409 decimal 6 01/08/14

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