INFORMATION

CONVERSION FROM DECIMAL TO OTHER BASES

WHOLE NUMBERS

We apply the following rules to convert a decimal number to other bases.

• We divide the decimal number by the base 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 88 to octal (base 8), we divide 88 by 8 repeatedly until the quotient becomes 0.

When we divide 88 by 8, the quotient is 11 and the remainder is 0. Thus, 0 is the least significant digit of the octal equivalent. We continue the algorithm with 11. When we divide 11 by 8, the quotient is 1 and the remainder is 3. Then 3 is the second least significant digit. Finally, we divide 1 by 8. 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 octal number. To sum up, the octal representation of 88 is 130.

(88)₁₀ = (130)₈

DECIMAL NUMBERS

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

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

• We multiply the fractional part by the base 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 number in toher base. We continue with the fractional part of the product.

For example, to convert 88.37 to octal (base 8), we multiply the fractional part by 8 repeatedly.

• 0.37 × 8 = 2.96
• 0.96 × 8 = 7.68
• 0.68 × 8 = 5.44
• .........................

The fractional part of 88.37 is 0.37. When we multiply 0.37 by 8, the result is 2.96. The integer part of 2.96 is 2. Thus we write 2 to the first digit on the RHS of the decimal point.

0.2

We continue with the fractional part of 2.96. When we multiply 2.96 by 8, the result is 7.68. We write the integer part of 7.68 to the next digit of the octal.

0.27

The fractional part of 7.68 is 0.68. Therefore, we continue with this number. The product of 0.68 and 8 is equal to 5.44. We write the integer part to the next digit.

(0.37)₁₀ = (0.275...)₈

Octal representation of 88.37 is equal to the sum of octal representations of 88 and 0.37. Thus, decimal 88.37 is equal to octal 130.275....

(88.37)₁₀ = (88)₁₀ + (0.37)₁₀

= (130)₈ + (0.275...)₈

= (130.275...)₈

WHAT IS BASE CONVERTER DECIMAL TO OTHER BASES?

Base converter - decimal to other bases, computes the equivalent of the entered decimal number in bases from 2 to 16.

HOW TO USE BASE CONVERTER DECIMAL TO OTHER BASES?

You can use this 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 equivalents of other decimals you can clear the input box by clicking on the CLEAR button under the input box.

• COPYING & DOWNLOADING THE SOLUTION

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

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    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.