INFORMATION

DECIMAL TO BASE 14 CONVERSION

WHOLE NUMBERS

We apply the following rules to convert a decimal number to base 14.

• We divide the decimal number by 14 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 380 to base 14, we divide 380 by 14 repeatedly until the quotient becomes 0.

When we divide 380 by 14, the quotient is 27 and the remainder is 2. Thus, 2 is the least significant digit of the base 14 equivalent. We continue the algorithm with 27. When we divide 27 by 14, the quotient is 1 and the remainder is 13. Because 13 is equivalent to D in base 14, we write D to the second least significant digit. Finally, we divide 1 by 14. 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 14 number. To sum up, the base 14 representation of 380 is 1D2.

(380)₁₀ = (1D2)₁₄

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 14 equivalents up.

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

• We multiply the fractional part by 14 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 14 number. We continue with the fractional part of the product.

For example, to convert 380.75 to base 14, we multiply the fractional part by 14 repeatedly until we find an integer.

• 0.75 × 14 = 10.5
• 0.5 × 14 = 7

The fractional part of 380.75 is 0.75. When we multiply 0.75 by 14, the result is 10.5. The integer part of 10.5 is 10. Because 10 is equivalent to A in base 14, we write A to the first digit on the RHS of the radix point.

0.A

We continue with the fractional part of 10.5. When we multiply 0.5 by 14, the result is 7. Because 7 is an integer, we write it to the next digit of the base 14 number and stop multiplications.

(0.75)₁₀ = (0.A7)₁₄

Base 14 representation of 380.75 is equal to the sum of base 14 representations of 380 and 0.75. Thus, decimal 380.75 is equal to 1D2.A7 in base 14.

(380.75)₁₀ = (380)₁₀ + (0.75)₁₀

= (1D2)₁₄ + (0.A7)₁₄

= (1D2.A7)₁₄

WHAT IS DECIMAL TO BASE 14 CONVERTER?

Decimal to base 14 converter,

• Computes the base 14 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 14 CONVERTER?

You can use decimal to base 14 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 14 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.