Binary to Octal Converter
Binary to Octal Converter. Enter your binary string and the Binary to Octal Converter instantly returns the matching value in Octal Output. For checking file mode bits or older octal-based specs, the hex to octal converter turns a hex input straight into readable octal output.
Got a long string of ones and zeros and need its base 8 form? The binary to octal converter turns any binary number into its octal equivalent in a single click, so you never have to regroup bits by hand. Each octal digit stands for exactly three binary digits, which is why computers and electronics engineers still lean on this shortcut.
How to Use the Binary to Octal Converter
Using the tool takes about five seconds. Type or paste a binary number into the input box, using only the symbols 0 and 1. A leading minus sign is accepted as a negative sign, and a binary point lets you enter a fractional value such as 101101.0111. Then press the Convert button and the octal result appears below the field.
- Press the Clear button to empty the box before checking another value.
- Use Copy to place the octal answer on your clipboard for a spreadsheet, a script or a homework file.
- Try a random binary number when you want fresh practice material and a quick way to test your own mental grouping.
This kind of number conversion follows the same grouping rule you can run on paper, so every answer is easy to double-check. The sections below show the full solution step by step, and the lookup table further down covers every pairing, so you can verify any output yourself.
Convert Binary to Octal Without a Tool
To convert binary to octal by hand, you only need the eight three-bit patterns in the chart further down. Split the number into blocks, swap each block for its single octal symbol, and read the digits left to right. Nothing about the process needs a calculator, which is exactly why it appears in so many mathematics and computer science courses.
Binary to Octal Conversion: The Direct Method
The direct method works because 8 equals 2 cubed, so one octal digit always carries the same information as three bits. Start at the rightmost bit, the LSB, and cut the string into groups of three. If the leftmost group has fewer than three bits, pad it with zeros on the left until it is a full group of three.
Each block of three bits is then read using the place weights 4, 2 and 1, which are the powers of 2 from \(2^{2}\) down to \(2^{0}\):
$$d = 4 \times b_{2} + 2 \times b_{1} + 1 \times b_{0}$$
Here \(b_{2}\), \(b_{1}\) and \(b_{0}\) are the three bits of one block, and \(d\) is the resulting octal symbol from 0 to 7. These weights are why the 111 block becomes 7 and the 101 block becomes 5.
Handling the Radix Point and Fractional Part
A number with a radix point is split in two directions. In the integer part, you group from the radix point leftward and pad the leftmost group on its left. In the fractional part, you group from the point rightward and pad the final group with zeros on its right. The point itself stays where it is, so a fractional binary number simply becomes a fractional octal number.
Binary Octal Conversion Chart and Worked Examples
Keep this lookup handy, because it holds every pairing you will ever need for base 2 and base 8. Memorize it once and nearly every conversion becomes a reading exercise.
Binary Octal Conversion Chart for Three-Bit Groups
| Binary | Octal | Decimal |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
Binary to Octal Conversion Examples
These solved examples use inputs of our own. The first has ten bits, so the leftmost block needs two padding zeros. The second has a fractional part, so both ends need attention.
| Binary number | Grouped in threes | Octal number |
|---|---|---|
| 1011110101 | 001 011 110 101 | 1365 |
| 101101.0111 | 101 101 . 011 100 | 55.34 |
| 110010011 | 110 010 011 | 623 |
Take the first row and its solution. The string 1011110101 has a single bit left over on the left, so 001 completes the leftmost block. The blocks 001, 011, 110 and 101 read as 1, 3, 6 and 5, giving 1365 in base 8. In the second row, 0111 after the point splits into 011 and 1, and the lone 1 becomes 100 after two zeros are appended on the right, which gives 55.34.
Convert Binary to Octal Through Decimal
When a number does not fall neatly into blocks, or you want a second opinion, route the work through base 10. This indirect path combines binary to decimal and decimal to octal steps, and it is the version most textbooks teach first.
- Multiply each bit by its power of 2 and add the products. This gives the decimal equivalent.
- Apply division by 8 to that decimal value, noting the remainder each time.
- Keep dividing the quotient until it reaches zero.
- Write remainders in reverse order, with the last one first. The final remainder is the leading digit of the answer.
Using 1011110101 again: \(512 + 128 + 64 + 32 + 16 + 4 + 1 = 757\). Dividing, 757 ÷ 8 leaves 5 with quotient 94, 94 ÷ 8 leaves 6 with quotient 11, 11 ÷ 8 leaves 3 with quotient 1, and 1 ÷ 8 leaves 1. Reading the remainders from the last to the first gives 1365, which matches the direct method exactly.
$$1011110101_{2} = 757_{10} = 1365_{8}$$
Checking a Permission Mask with the Binary to Octal Converter
Dariusz is tightening a shared deployment folder on a Linux build server. A security review says only the owner may write, the group may read and enter, and everyone else gets nothing. His notes already list the intended permission bits as a nine-character string: 111101000, meaning read, write and execute for the owner, read and execute for the group, and no access for others.
The chmod command wants those nine bits as three octal digits, so he pastes 111101000 into the input box and presses the Convert button. The tool splits the string into 111, 101 and 000, and the result shows 750.
- 111 gives 7, the owner's read, write and execute.
- 101 gives 5, the group's read and execute, with the write bit off.
- 000 gives 0, so others have no access at all.
The decimal equivalent is 488, but nothing in the POSIX file-permission scheme uses that number, which is why the octal form matters here. Each three-bit group becomes one octal digit, so the converter hands him the exact value chmod expects. Dariusz compares 750 against the review's wording and sees an exact match: owner full control, group read and execute, others locked out.
Before running anything he changes one bit. The auditor mentions that a deploy bot sits in the group and must also write logs, so he flips the group's middle bit and enters 111111000. The result jumps to 770, which grants the group write access without opening anything to others. He picks 770 for the shared folder and keeps 750 for the release directory the bot only reads.
Why Binary to Octal Conversion Works: Number System Basics
A number system is defined by its base, also called the radix. Each numeral system here is positional, which means the value of a digit depends on where it sits. The same positional system idea powers the decimal numbers you use every day.
Binary Number System
The binary number system uses base 2 and only two symbols, 0 and 1. Each binary digit, called a bit, maps neatly onto an on or off state, such as an electric signal that is high or low. That is the reason digital data, from code to photos, is stored as bits and bytes inside every machine.
Octal Number System
The octal number system uses base 8 and the symbols 0 through 7, so an octal number never contains an 8 or a 9. Early computing favoured it because some machines used word sizes divisible by three, such as 12, 24 or 36 bits, and each word split cleanly into octal digits. Even today, programming tasks such as setting Unix file permissions rely on it.
Binary to Octal Conversion Tool Versus Other Base Converters
Octal is one stop among several base converters. Going back the other way is the job of an octal to binary converter, which expands every octal digit into its three-bit pattern. Hexadecimal works the same way with four bits per symbol, so a hexadecimal number is shorter still. A good base converter handles all of these in one place, and programmers often shorten hex values the same way when reading memory dumps.
Common Mistakes in Binary to Octal Grouping
When you group bits by hand, most wrong answers trace back to the same few slips. Grouping from the left instead of the right shifts every block and changes the whole result, so always anchor your grouping at the rightmost bit of the integer part. Forgetting to pad a short final block is the next most common error, and it quietly turns 1 into 100 or 4 into 1 depending on which side lacks the zeros.
A third slip is writing the digits 8 or 9 in an octal answer, which signals an arithmetic error because base 8 stops at 7. Finally, when you check the answer through decimal, remember that the remainders come out backwards, so reverse them before writing the final value. Running the tool alongside your own working catches all four problems in seconds, and it is a reliable way to build confidence before an exam or a code review.
Practice Questions on Binary to Octal Conversion
Test yourself, then check each answer with the tool:
- Convert 100111010 to octal.
- Convert 11110001 to octal, remembering to pad the leftmost group.
- Convert 0.101011 to octal, grouping to the right of the point.
The answers are 472, 361 and 0.53. If you miss one, redo the grouping slowly and compare it to the three-bit chart above.