# ⇩ BASE N TO DECIMAL CONVERTERS ⇩

#### OCTAL TO DECIMAL CONVERTER (WITH STEPS)

Enter an octal number.

(125)8 = (85)10

SOLUTION

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 ⇩

## 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.

... ... ...

...

...

...

### 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

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.

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

• 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.