DECIMAL TO BASE 11 CONVERSION
We apply the following rules to convert a decimal number to base 11.
- We divide the decimal number by 11 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 824 to base 11, we divide 824 by 11 repeatedly until the quotient becomes 0.
When we divide 824 by 11, the quotient is 74 and the remainder is 10.
Because 10 is represented with letter "A" in base 11, "A" is the least significant digit of the base 11 number.
We continue the algorithm with 74.
When we divide 74 by 11, the quotient is 6 and the remainder is 8. Then 8 is the second least significant digit of the base 11 number.
Finally, we divide 6 by
11. When we do this operation, the quotient is 0 and the remainder is 6. Because the quotient is 0, we stop the procedure. Then we write the last
remainder to the most significant digit of the base 11 number. To sum up, the base 11 representation of 824 is 68A.
(824)10 = (68A)11
In case, the decimal number is not an integer, we can convert the whole number and fractional parts separately and add the base 11 equivalents up.
To convert the fractional part of a decimal number, we apply the following rules.
- We multiply the fractional part by 11 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 11 number. We continue with the fractional part of the product.
For example, to convert 824.36 to base 11, we multiply the fractional part by 11 repeatedly.
- 0.36 × 11 = 3.96
- 0.96 × 11 = 10.56
- 0.56 × 11 = 6.16
The fractional part of 824.36 is 0.36. When we multiply 0.36 by 11, the result is 3.96. The integer part of
3.96 is 3. Thus we write 3 to the first digit on the RHS of the radix point.
We continue with the fractional part of 3.96. When we multiply 0.96 by 11, the result is 10.56. We write the integer part of
10.56 to the next digit of the base 11 number. Because 10 is represented with letter "A" in base 11, we write "A" to the next digit.
The fractional part of 10.56 is 0.56. Therefore, we continue with this number. The product of 0.56 and 11 is equal to 6.16.
We write it to the next digit of the base 11 number.
(0.36)10 = (0.3A6...)11
Base 11 representation of 824.36 is equal to the sum of base 11 representations of 824 and 0.36. Thus, decimal 824.36 is equal to
68A.3A6... in base 11.
(824.36)10 = (824)10 + (0.36)10
= (68A)11 + (0.3A6...)11
WHAT IS DECIMAL TO BASE 11 CONVERTER?
Decimal to base 11 converter,
- Computes the base 11 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 11 CONVERTER?
You can use decimal to base 11 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 11 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.