Octal Number

Octal numbers use digits from 0-7 only. It is known as base-8 number. The place value of each digits of an octal number varies as the whole number powers of 8 starting from the right (Least Significant Digit). The first single digit number in octal system is 0 and the last is 7. Similarly, the first two digit octal number is 10 and the last is 77 and so on. Octal number system was widely used in early computers.

Decimal Number

Whole number, a decimal point and a fractional value combines to form a decimal number. The decimal point separates the whole number part from the fractional part of the number. Each digit of a decimal number can be any number from 0 to 9. Any value less than 1 is written to the right of decimal point. Decimal numbers are also known as base-10 number or counting numbers. Place value of decimal number varies as the whole number powers of 10 starting from the left of decimal point. Similarly, the place value of digits left to decimal point varies as the division of power of tens.

How to convert octal to decimal

Step 1:

To convert octal number to a decimal number, first of all, we have to list down each digit one below the other starting from the left.

Step 2:

Count the digit from the top to bottom. The count must start from 0.

Step 3:

Multiply each digit by 8 to the power of its position count.

Step 4:

Add all the values you calculated in the previous step. The sum gives the decimal value corresponding to the octal value.
In-short:
Octal number can be converted into decimal number using the following formula:

Decimal Number = (D_n X 8ⁿ + …………… + D₂ X 8² + D₁ X 8¹ + D₀ X 8⁰).

Where,

Dn – D0 → digits of a octal number.
n → Position count starting from 0 (left to right).

Use Octal to Decimal convertor

Example 1:

Convert 5658 to decimal

Decimal number = 5 X 8² + 6 X 8¹ + 5 X 8⁰= 5 X 64 + 6 X 8 + 5 =384 + 48 + 5 = 447₁₀

Example 2:

Convert 7778 to decimal

Decimal number = 7 X 8² + 7 X 8¹ + 7 X 8⁰= 7 X 64 + 7 X 8 + 7 = 448 + 56 + 7 = 511₁₀

Octal to Decimal conversion table