BASIC MATH CALCULATORS


TOOL: OCTAL TO DECIMAL CONVERTER (WITH STEPS)


BASE N TO DECIMAL CONVERTERS

23456789111213141516

OCTAL TO DECIMAL CONVERTER (WITH STEPS)

Enter an octal number.


(125)8 = (85)10

SOLUTION

1255x802x811x82Place Value

We multiply each digit by its place value and add the products.

(125)8 = (1 × 82) + (2 × 81) + (5 × 80)

= (1 × 64) + (2 × 8) + (5 × 1)

= 64 + 16 + 5

= (85)10

OTHER INFORMATION

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BASE N TO DECIMAL CONVERTERS

23456789111213141516

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.

Octal number place values

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.

... ... ...

...

...

...

OCTAL TO DECIMAL CONVERSION TABLE

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

08 = 010

18 = 110

28 = 210

38 = 310

48 = 410

58 = 510

68 = 610

78 = 710

108 = 810

118 = 910

128 = 1010

138 = 1110

148 = 1210

158 = 1310

168 = 1410

178 = 1510

208 = 1610

218 = 1710

228 = 1810

238 = 1910

248 = 2010

258 = 2110

268 = 2210

278 = 2310

308 = 2410

318 = 2510

328 = 2610

338 = 2710

348 = 2810

358 = 2910

368 = 3010

378 = 3110

408 = 3210

418 = 3310

428 = 3410

438 = 3510

448 = 3610

458 = 3710

468 = 3810

478 = 3910

508 = 4010

518 = 4110

528 = 4210

538 = 4310

548 = 4410

558 = 4510

568 = 4610

578 = 4710

608 = 4810

618 = 4910

628 = 5010

638 = 5110

648 = 5210

658 = 5310

668 = 5410

678 = 5510

708 = 5610

718 = 5710

728 = 5810

738 = 5910

748 = 6010

758 = 6110

768 = 6210

778 = 6310

1008 = 6410

1018 = 6510

1028 = 6610

1038 = 6710

1048 = 6810

1058 = 6910

1068 = 7010

1078 = 7110

1108 = 7210

1118 = 7310

1128 = 7410

1138 = 7510

1148 = 7610

1158 = 7710

1168 = 7810

1178 = 7910

1208 = 8010

1218 = 8110

1228 = 8210

1238 = 8310

1248 = 8410

1258 = 8510

1268 = 8610

1278 = 8710

1308 = 8810

1318 = 8910

1328 = 9010

1338 = 9110

1348 = 9210

1358 = 9310

1368 = 9410

1378 = 9510

1408 = 9610

1418 = 9710

1428 = 9810

1438 = 9910

1448 = 10010

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

    Convert button

    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

    Random button-convert

    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

    Clear button-two inputs

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

  • COPYING & DOWNLOADING THE SOLUTION

    • Copy Link

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

    • Download Link

      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.

 

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