DECIMAL TO BASE 15 CONVERSION
We apply the following rules to convert a decimal number to base 15.
- We divide the decimal number by 15 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 856 to base 15, we divide 856 by 15 repeatedly until the quotient becomes 0.
When we divide 856 by 15, the quotient is 57 and the remainder is 1. Thus, 1 is the least significant digit of the base 15 equivalent.
We continue the algorithm with 57.
When we divide 57 by 15, the quotient is 3 and the remainder is 12. Because 12 is equivalent to C in base 15, we write C to
the second least significant digit of the base.
Finally, we divide 3 by
15. When we do this operation, the quotient is 0 and the remainder is 3. Because the quotient is 0, we stop the procedure. Then we write the last
remainder to the most significant digit of the base 15 number. To sum up, the base 15 representation of 856 is 3C1.
(856)10 = (3C1)15
In case, the decimal number is not an integer, we can convert the whole number and fractional parts separately and add the base 15 equivalents up.
To convert the fractional part of a decimal number, we apply the following rules.
- We multiply the fractional part by 15 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 15 number. We continue with the fractional part of the product.
For example, to convert 856.16 to base 15, we multiply the fractional part by 15 repeatedly until we find an integer.
- 0.16 × 15 = 2.4
- 0.4 × 15 = 6
The fractional part of 856.16 is 0.16. When we multiply 0.16 by 15, the result is 2.4. The integer part of
2.4 is 2. Thus we write 2 to the first digit on the RHS of the radix point.
We continue with the fractional part of 2.4. When we multiply 0.4 by 15, the result is 6. Because
6 is an integer we write it to the next digit of the base 15 number and stop multiplications.
(0.16)10 = (0.26)15
Base 15 representation of 856.16 is equal to the sum of base 15 representations of 856 and 0.16. Thus, decimal 856.16 is equal to
3C1.16 in base 15.
(856.16)10 = (856)10 + (0.16)10
= (3C1)15 + (0.16)15
WHAT IS DECIMAL TO BASE 15 CONVERTER?
Decimal to base 15 converter,
- Computes the base 15 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 15 CONVERTER?
You can use decimal to base 15 converter in two ways.
You can enter a decimal number to the input box and click on the "CONVERT" button. The result and
explanations appaer below the calculator
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 15 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.