Convert Octal to Decimal
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How to convert octal to decimal

To convert an octal number (base-8) to the decimal (base-10) number system, we need to use octal place value to add the base-10 value of each digit.

In the octal place value system, each time you move a place to the left, the value increases eight-fold.

In octal, the digit values go from zero to seven; numbers 8 and 9 are not allowed!

This table above shows the number 326,107 in the octal number system.

1) Convert 275 from octal to decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

(2 x 64) + (7 x 8) + (5 x 1)

= 128 + 56 + 5 = 189

So 275 in octal is equal to 189.

2) Convert 3250 from octal into decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

(3 x 512) + (2 x 64) + (5 x 8) + (0 x 1)

1536 + 128 + 40 + 0 = 1704

So 3250 in octal is equal to 1704.

How to convert from decimal to octal

To convert a decimal number (base-10) to the octal (base-8) number system, we need to change the decimal base-10 place value into octal base-8 place value.

We can do this in different ways by using division and looking at quotients and remainders.

The best way to see this is to look at some worked examples .

Example 1) Convert 139 from decimal to octal.

Step 1) Look at what octal place values we need.

The powers of 8 are 1, 8, 64, 512, 4096, ...

Our value is just 139, so the powers of 8 we need are 1, 8 and 64 (up to 8²).

Step 2) Divide 139 by the highest place value number.

So we now divide 139 by 64 = 2 r. 11

The quotient tells us what number goes into with the place value of 64, which is 2.

Step 3) We now divide the remainder by the next (lower) power of 8.

So we have 11 ÷ 8 = 1 r. 3

The quotient us what number goes with the place value of 8, which is 1.

Step 4) Divide the remainder by the next (lower) power of 8.

So we have 3 ÷ 1 = 3

This tells us which number goes with the place value of 1s which is 3.

Step 5) Put your place value parts together.

Our number 139 = (2 x 64) + (1 x 8) + (3 x 1).

So our octal answer is 213.

Example 2) Convert 946 from decimal to octal.

Step 1) Look at what octal place values we need.

The powers of 8 are 1, 8, 64, 512, 4096, ...

Our value is just 946, so the powers of 8 we need are 1, 8, 64 and 512(up to 8³).

Step 2) Divide 946 by the highest place value number.

So we now divide 946 by 512 = 1 r. 434

The quotient tells us what number goes into with the place value of 512, which is 1.

Step 3) We now divide the remainder by the next (lower) power of 8.

So we have 434 ÷ 64 = 6 r. 50

The quotient us what number goes with the place value of 64, which is 6.

Step 4) We now divide the remainder by the next (lower) power of 8.

So we have 50 ÷ 8 = 6 r. 2

The quotient us what number goes with the place value of 8, which is 6.

Step 5) We now divide the remainder by the next (lower) power of 8.

So we have 2 ÷ 1 = 2

The quotient us what number goes with the place value of 1s, which is 2.

Step 6) Put your place value parts together.

Our number 946 = (1 x 512) + (6 x 64) + (6 x 8) + (2 x 1).

So our octal answer is 1662.