How to Convert Base 10 to Base 16

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Base 10, also known as the decimal system, is the ordinary base we use every day. Base 16, also known as the hexadecimal system, is used by computer scientists because 16 is a power of 2 and computers are based on binary, or base 2 arithmetic. In base 10, the rightmost digit in a number represents units, the next digit 10s and so on. Thus 312 (10) = 3100 + 110 + 21. In base 16, the rightmost digit is again units, the next digit 16, the next 256s (1616) and so on. Thus, 312 (16) = 3256 (10) + 116 (10) + 2*1 = 784 (10). Digits above 10 are represented by letter A through F.

  • Divide the number you wish to convert by 16 and write the quotient and remainder. For instance, if you want to convert 543 (10) to base 16, divide 543 by 16 and write 33 R 15.

  • Divide the quotient from Step 1 by 16 and again write the quotient and remainder. So divide 33 by 16 and write 2 R 1.

  • Continue this process until the quotient is 0. In our example, divide 1 by 16 and get 0 R 2.

  • Convert remainders as needed. If any of the remainders are 10 or higher, write A for 10, B for 11, C for 12, D for 13, E for 14 or F for 15. In our example, the first remainder was 15, so convert it to F.

  • Write the remainders in reverse order that you got them. In our example, 21F. This is the solution. 543 (10) = 21F (16).

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