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The Magic of Remainders
Hook about how remainders build the new number.
When breaking down a base-10 number into another base, the leftover pieces (the remainders) literally build your new number from the ground up!
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The Repeated Division Method
Explain the 4 steps to convert decimal to any base.
Converting a decimal (base-10) number to binary, octal, or hexadecimal might seem complex, but it relies on one universal algorithm: repeated division.
Step 1 & 2: Divide and Note
Step 1: Divide your given decimal number by the base value () of the target number system (e.g., 2 for binary, 8 for octal, 16 for hex).
Step 2: Note the remainder of this division. This remainder becomes part of your newly converted number.
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Decimal to Binary Example
Visual of 65 divided by 2.
Click to zoom
Repeatedly divide by 2, collect remainders bottom-up.
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Watch Out for Hexadecimal!
Explain how to handle remainders greater than 9 in Hex.
The exact same method works for base 8 and base 16. You just swap out the divisor. However, hexadecimal introduces a unique challenge you must watch out for.
The Hex Alphabet Rule
If your division yields a remainder of 10, 11, 12, 13, 14, or 15, you MUST convert it to its Hexadecimal symbol (A, B, C, D, E, F) before writing your final answer. Leaving it as a two-digit decimal will ruin your conversion.
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Practice: Decimal to Octal
Fill blanks for converting 65 to Octal.
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To convert the decimal number 65 to its octal equivalent, you must repeatedly divide the number by the base value, which is. In the first step, dividing 65 by 8 yields a quotient ofand a remainder of 1. Next, you take that quotient and divide it by 8 again, which gives a new quotient of 1 and a remainder of. Finally, dividing 1 by 8 results in a quotient of 0 and a remainder of. Once the quotient reaches zero, you stop the division process and collect the recorded remainders. By reading these remainders from bottom to top, you get the final octal answer, which is.
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Test Your Conversion
Convert 122 to binary.
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Based on the repeated division process, what is the binary equivalent of the decimal number 122?