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Octal to Binary: Definition and Examples | EDU.COM

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Octal to Binary: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Octal to BinaryOctal to Binary: Definition and ExamplesTable of ContentsOctal to Binary Conversion Definition of Octal to Binary Conversion

Octal to binary conversion means changing a number from base-8 (octal) to base-2 (binary). The octal number system uses digits 0 through 7, while the binary system only uses 0 and 1 (called bits). Each octal digit can be represented by exactly three binary digits, which makes conversion between these systems quite straightforward.

The binary number system forms the foundation of all computer operations and uses only two digits: 0 and 1. The octal number system, with its base of 8, is commonly used in minicomputers and programming. Both systems have important applications in computing, with the octal system serving as a more compact way to represent binary data, as each octal digit represents three binary bits.

Examples of Octal to Binary Example 1: Direct Method Using Conversion Table Problem:

Convert 54854_8548​ to binary using the direct method.

Step-by-step solution:

Step 1, Break down the octal number into individual digits: 555 and 444.

Step 2, Find the 3-digit binary equivalent for each octal digit:

5→1015 \rightarrow 1015→101 4→1004 \rightarrow 1004→100

Step 3, Combine these binary values to get your answer: 548=101100254_8 = 101100_2548​=1011002​

Example 2: Converting Octal to Binary Without Using the Table Problem:

Convert 7658765_87658​ to binary without using the conversion table.

Step-by-step solution:

Step 1, Write down the octal digits separately: 7, 6, 5.

Step 2, For each digit, write the values of the binary place holders: 4, 2, 1 (representing 222^222, 212^121, 202^020).

Step 3, For each octal digit, check which values from 4, 2, 1 sum up to that digit:

For 7: 7=4+2+17 = 4 + 2 + 17=4+2+1, so write 1 under each value: 111 For 6: 6=4+2+06 = 4 + 2 + 06=4+2+0, so write 1, 1, 0: 110 For 5: 5=4+1+05 = 4 + 1 + 05=4+1+0, so write 1, 0, 1: 101

Step 4, Combine all binary digits from left to right: 7658=1111101012765_8 = 111110101_27658​=1111101012​

Example 3: Indirect Method Using Decimal Conversion Problem:

Convert 52852_8528​ to binary using the indirect decimal conversion method.

Step-by-step solution:

Step 1, Convert octal to decimal first:

528=2×80+5×8152_8 = 2 \times 8^0 + 5 \times 8^1528​=2×80+5×81 =2×1+5×8= 2 \times 1 + 5 \times 8=2×1+5×8 =2+40= 2 + 40=2+40 =4210= 42_{10}=4210​

Step 2, Convert the decimal number to binary by dividing by 2 repeatedly:

42÷2=2142 ÷ 2 = 2142÷2=21 with remainder 000 21÷2=1021 ÷ 2 = 1021÷2=10 with remainder 111 10÷2=510 ÷ 2 = 510÷2=5 with remainder 000 5÷2=25 ÷ 2 = 25÷2=2 with remainder 111 2÷2=12 ÷ 2 = 12÷2=1 with remainder 000 1÷2=01 ÷ 2 = 01÷2=0 with remainder 111

Step 3, Read the remainders from bottom to top to get the binary number: 4210=101010242_{10} = 101010_24210​=1010102​

Step 4, So our final answer is: 528=101010252_8 = 101010_2528​=1010102​

Comments(2)CCarEnthusiastJakeNovember 5, 2025This page on octal to binary is great! I've used it to help my students understand the conversions. The examples are really clear.

TTeacherAmyNovember 4, 2025This page on octal to binary is great! I've used it to help my students. The methods and examples make it easy to understand.

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