INFORMATION

DECIMAL TO BASE 13 CONVERSION

WHOLE NUMBERS

We apply the following rules to convert a decimal number to base 13.

• We divide the decimal number by 13 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 336 to base 13, we divide 336 by 13 repeatedly until the quotient becomes 0.

When we divide 336 by 13, the quotient is 25 and the remainder is 11. Because 11 is equivalent to B in base 13, we write B to the least significant digit of the base 13 number. We continue the algorithm with 25. When we divide 25 by 13, the quotient is 1 and the remainder is 12. Becasue 12 is equivalent to C in base 13, we write C to the second least significant digit. Finally, we divide 1 by 13. When we do this operation, the quotient is 0 and the remainder is 1. Because the quotient is 0, we stop the procedure. Then we write the last remainder to the most significant digit of the base 13 number. To sum up, the base 13 representation of 336 is 1CB.

(336)₁₀ = (1CB)₁₃

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 13 equivalents up.

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

• We multiply the fractional part by 13 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 13 number. We continue with the fractional part of the product.

For example, to convert 336.06 to base 13, we multiply the fractional part by 13 repeatedly.

• 0.06 × 13 = 0.78
• 0.78 × 13 = 10.14
• 0.14 × 13 = 1.82
• ........................

The fractional part of 336.06 is 0.06. When we multiply 0.06 by 13, the result is 0.78. The integer part of 0.78 is 0. Thus we write 0 to the first digit on the RHS of the radix point.

0.0

We continue with the fractional part of 0.78. When we multiply 0.78 by 13, the result is 10.14. Because 10 is equivalent to A in base 13 we write A to the next digit.

0.0A

The fractional part of 10.14 is 0.14. Therefore, we continue with this number. The product of 0.14 and 13 is equal to 1.82. We write 1 to the next digit.

(0.06)₁₀ = (0.0A1...)₁₃

Base 13 representation of 336.06 is equal to the sum of base 13 representations of 336 and 0.06. Thus, decimal 336.06 is equal to 1CB.0A1... in base 13.

(336.06)₁₀ = (336)₁₀ + (0.06)₁₀

= (1CB)₁₃ + (0.0A1...)₁₃

= (1CB.0A1...)₁₃

WHAT IS DECIMAL TO BASE 13 CONVERTER?

Decimal to base 13 converter,

• Computes the base 13 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 13 CONVERTER?

You can use decimal to base 13 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 13 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.