INFORMATION

HEXADECIMAL AND DECIMAL NUMBERS

Binary, octal, decimal and hexadecimal numbering systems are commonly used in mathematics, computer science and electrical engineering.

Octal Numbering System (Base 8): In the octal numbering system, numbers are represented by eight digits: 0, 1, 2, 3, 4, 5, 6 and 7. The ones digit has a place value of 8⁰ = 1, the next digit to the left has a place value of 8¹ = 8, then 8² = 64, and so on. As we move one place to the left, the place value increases by a factor of 8.

Decimal Numbering System (Base 10): In the decimal system, numbers are represented using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit has a place value of 10 raised to a power depending on its position in the number.

OCTAL TO DECIMAL CONVERSION

Each octal number has a unique representation in other numbering systems. Octal to decimal (oct to dec) conversion is the process of computing the equivalent decimal representation of a base 8 (octal) number. To convert an octal number to decimal we multiply each digit by its place value and add the products.

Each place value in octal representation corresponds to an exponent of 8. The exponent increases by 1 as we move one digit to the left, starting from zero for the ones digit.

BINARY TO DECIMAL CONVERSION EXAMPLES

EXAMPLE:

Find the decimal equivalent of 503₈.

To find the decimal equivalent of this number, we multiply each digit by its place value and then sum up the products.

503₈ = 5 · 8² + 0 · 8¹ + 3 · 8⁰

= 5 · 64 + 0 · 8 + 3 · 1

= 320 + 0 + 3

= 323₁₀

So, the decimal equivalent of 503₈ is 323₁₀.

EXAMPLE:

Find the decimal equivalent of the 47.2₈.

The place values of B0.4₁₆ are shown below.

Multiply those values with the corresponding digits and add the products.

$\mathrm{47.2_{8}}$ $\mathrm{=4\cdot8+7\cdot1+}$ $\mathrm{2\cdot\dfrac{1}{8}}$

$\mathrm{=32+7+\dfrac{2}{8}}$

$\mathrm{=39\cdot\dfrac{1}{4}}$

$\mathrm{=39.25_{10}}$

OCTAL TO DECIMAL CONVERSION TABLE

The table below displays the decimal equivalents of the smallest non-negative octal numbers up to 100.

WHAT IS OCTAL TO DECIMAL CONVERTER?

Octal to decimal converter,

• Computes the decimal equivalent of the entered octal number,
• Describes the solution step by step and
• Illustrates the place values.

HOW TO USE OCTAL TO DECIMAL CONVERTER?

You can use octal to decimal converter in two ways.

• USER INPUTS

  

  You can enter an octal number into the input box and then click the 'CONVERT' button. The result and explanations will appear below the calculator.

• RANDOM INPUTS

  

  You can click on the DIE ICON next to the input box to generate a random octal number, which will be automatically entered into the calculator. The result and explanations will then appear below the calculator. You can also create your own examples and practice using this feature.

• CLEARING THE INPUT BOX

  

  To find the decimal equivalent of another hexadecimal number, click on the CLEAR button to clear the input box.

• COPYING & DOWNLOADING THE SOLUTION

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    You can copy the generated solution by clicking on the 'Copy Text' link located below the solution panel.

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    You can also download the solution as an image file with a .jpg extension by clicking on the 'Download Solution' link located at the bottom of the solution panel. You can then share the downloaded image file.