INFORMATION

DECIMAL TO BASE 12 CONVERSION

WHOLE NUMBERS

We apply the following rules to convert a decimal number to base 12.

• We divide the decimal number by 12 repeatedly until the quotient becomes 0.
• Starting at the least significant digit, we write the remainders in the same order of divisions.

For example, to convert decimal 421 to base 12, we divide 421 by 12 repeatedly until the quotient becomes 0.

When we divide 421 by 12, the quotient is 35 and the remainder is 1. Thus, 1 is the least significant digit of the base 12 equivalent. We continue the algorithm with 35. When we divide 35 by 12, the quotient is 2 and the remainder is 11. Because 11 is equivalent to "B" in base 12 we write "B" to the next digit. Finally, we divide 2 by 12. When we do this operation, the quotient is 0 and the remainder is 2. Because the quotient is 0, we stop the procedure. Then we write the last remainder to the most significant digit of the base 12 number. To sum up, the base 12 representation of 421 is 2B1.

(421)₁₀ = (2B1)₁₂

DECIMAL NUMBERS

In case, the decimal number is not an integer, we can convert the whole number and fractional parts separately and add the base 12 equivalents up.

To convert the fractional part of a decimal number, we apply the following rules.

• We multiply the fractional part by 12 repeatedly until the product becomes an integer or the number of significant digits is sufficient for our calculations.
• At each step, we write the integer part of the rightmost digit to the fractional part of the base 12 number. We continue with the fractional part of the product.

For example, to convert 421.86 to base 12, we multiply the fractional part by 12 repeatedly.

• 0.86 × 12 = 10.32
• 0.32 × 12 = 3.84
• 0.84 × 12 = 10.08
• .......................

The fractional part of 421.86 is 0.86. When we multiply 0.86 by 12, the result is 10.32. The integer part of 10.32 is 10. Because 10 is equivalent to A in base 12, we write A to the first digit on the RHS of the radix point.

0.A

We continue with the fractional part of 10.32. When we multiply 0.32 by 12, the result is 3.84. We write the integer part of 3.84 to the next digit.

0.A3

The fractional part of 3.84 is 0.84. Therefore, we continue with this number. The product of 0.84 and 12 is equal to 10.08. Because 10 is equal to "A" in base 12, we write A to the next digit.

(0.86)₁₀ = (0.A3A...)₁₂

Base 12 representation of 421.86 is equal to the sum of base 12 representations of 421 and 0.86. Thus, decimal 421.86 is equal to 2B1.A3A... in base 12.

(421.86)₁₀ = (421)₁₀ + (0.86)₁₀

= (2B1)₁₂ + (0.A3A...)₁₂

= (2B1.A3A...)₁₂

WHAT IS DECIMAL TO BASE 12 CONVERTER?

Decimal to base 12 converter,

• Computes the base 12 equivalent of the entered decimal number and
• Describes each step of the conversion for both whole number and fractional parts,

HOW TO USE DECIMAL TO BASE 12 CONVERTER?

You can use decimal to base 12 converter in two ways.

• USER INPUTS

  

  You can enter a decimal number to the input box and click on the "CONVERT" button. The result and explanations appaer below the calculator

• RANDOM INPUTS

  

  You can click on the DIE ICON next to the input box. If you use this property, a random decimal number is generated and entered to the calculator, automatically. You can see the result and explanations below the calculator. You can create your own examples and practice using this property.

• CLEARING THE INPUT BOX

  

  To check the base 12 equivalent of other decimals you can clear the input box by clicking on the CLEAR button under the input box.

• COPYING & DOWNLOADING THE SOLUTION

  • 

    You can copy the generated solution by clicking on the "Copy Text" link, appaers under the solution panel.

  • 

    Even you can download the solution as an image file with .jpg extension if you click on the "Download Solution" link at the bottom of the solution panel. You can share the downloaded image file.