Octal to Decimal Converter
Enter an octal number.
(125)_{8} = (85)_{10}
SOLUTION
We multiply each digit by its place value and add the products.
(125)_{8} = (1 × 8^{2}) + (2 × 8^{1}) + (5 × 8^{0})
= (1 × 64) + (2 × 8) + (5 × 1)
= 64 + 16 + 5
= (85)_{10}
OTHER INFORMATION
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 8^{0} = 1, the next digit to the left has a place value of 8^{1} = 8, then 8^{2} = 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.
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.
Find the decimal equivalent of 503_{8}.
To find the decimal equivalent of this number, we multiply each digit by its place value and then sum up the products.
503_{8} = 5 · 8^{2} + 0 · 8^{1} + 3 · 8^{0}
= 5 · 64 + 0 · 8 + 3 · 1
= 320 + 0 + 3
= 323_{10}
So, the decimal equivalent of 503_{8} is 323_{10}.
Find the decimal equivalent of the 47.2_{8}.
The place values of B0.4_{16} are shown below.
Multiply those values with the corresponding digits and add the products.
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The table below displays the decimal equivalents of the smallest non-negative octal numbers up to 100.
0_{8} = 0_{10} |
1_{8} = 1_{10} |
2_{8} = 2_{10} |
3_{8} = 3_{10} |
4_{8} = 4_{10} |
5_{8} = 5_{10} |
6_{8} = 6_{10} |
7_{8} = 7_{10} |
10_{8} = 8_{10} |
11_{8} = 9_{10} |
12_{8} = 10_{10} |
13_{8} = 11_{10} |
14_{8} = 12_{10} |
15_{8} = 13_{10} |
16_{8} = 14_{10} |
17_{8} = 15_{10} |
20_{8} = 16_{10} |
21_{8} = 17_{10} |
22_{8} = 18_{10} |
23_{8} = 19_{10} |
24_{8} = 20_{10} |
25_{8} = 21_{10} |
26_{8} = 22_{10} |
27_{8} = 23_{10} |
30_{8} = 24_{10} |
31_{8} = 25_{10} |
32_{8} = 26_{10} |
33_{8} = 27_{10} |
34_{8} = 28_{10} |
35_{8} = 29_{10} |
36_{8} = 30_{10} |
37_{8} = 31_{10} |
40_{8} = 32_{10} |
41_{8} = 33_{10} |
42_{8} = 34_{10} |
43_{8} = 35_{10} |
44_{8} = 36_{10} |
45_{8} = 37_{10} |
46_{8} = 38_{10} |
47_{8} = 39_{10} |
50_{8} = 40_{10} |
51_{8} = 41_{10} |
52_{8} = 42_{10} |
53_{8} = 43_{10} |
54_{8} = 44_{10} |
55_{8} = 45_{10} |
56_{8} = 46_{10} |
57_{8} = 47_{10} |
60_{8} = 48_{10} |
61_{8} = 49_{10} |
62_{8} = 50_{10} |
63_{8} = 51_{10} |
64_{8} = 52_{10} |
65_{8} = 53_{10} |
66_{8} = 54_{10} |
67_{8} = 55_{10} |
70_{8} = 56_{10} |
71_{8} = 57_{10} |
72_{8} = 58_{10} |
73_{8} = 59_{10} |
74_{8} = 60_{10} |
75_{8} = 61_{10} |
76_{8} = 62_{10} |
77_{8} = 63_{10} |
100_{8} = 64_{10} |
101_{8} = 65_{10} |
102_{8} = 66_{10} |
103_{8} = 67_{10} |
104_{8} = 68_{10} |
105_{8} = 69_{10} |
106_{8} = 70_{10} |
107_{8} = 71_{10} |
110_{8} = 72_{10} |
111_{8} = 73_{10} |
112_{8} = 74_{10} |
113_{8} = 75_{10} |
114_{8} = 76_{10} |
115_{8} = 77_{10} |
116_{8} = 78_{10} |
117_{8} = 79_{10} |
120_{8} = 80_{10} |
121_{8} = 81_{10} |
122_{8} = 82_{10} |
123_{8} = 83_{10} |
124_{8} = 84_{10} |
125_{8} = 85_{10} |
126_{8} = 86_{10} |
127_{8} = 87_{10} |
130_{8} = 88_{10} |
131_{8} = 89_{10} |
132_{8} = 90_{10} |
133_{8} = 91_{10} |
134_{8} = 92_{10} |
135_{8} = 93_{10} |
136_{8} = 94_{10} |
137_{8} = 95_{10} |
140_{8} = 96_{10} |
141_{8} = 97_{10} |
142_{8} = 98_{10} |
143_{8} = 99_{10} |
144_{8} = 100_{10} |
Octal to decimal converter,
You can use octal to decimal converter in two ways.
You can enter an octal number into the input box and then click the '
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.
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.
Octal to Decimal Converter