How to Convert Octal to Binary: Steps, Table & Examples

The easiest way to convert octal to binary is to replace each octal digit with its equivalent 3-bit binary value, then join the groups together. For example, octal 157 becomes binary 1101111: 1 → 001, 5 → 101, 7 → 111. This works because octal is base 8, binary is base 2, and 8 = 2³ — so one octal digit always represents exactly three binary bits. This guide covers the full mapping table, a repeatable step-by-step process, and several verified examples of increasing difficulty.

What Is an Octal Number?

Octal is a base-8 number system. It uses only eight digit symbols — 0 through 7 — so a digit like 8 or 9 never appears in a valid octal number. Like decimal and binary, octal is a positional number system: each digit's value depends on its position, representing a power of 8 rather than a power of 10.

What Is a Binary Number?

Binary is a base-2 number system. It uses only two digit symbols, 0 and 1, commonly called bits. Every value a computer stores or processes is ultimately represented in binary, which is why converting other number systems — like octal — into binary is useful for reading raw bit-level data.

Why Is Octal Easy to Convert to Binary?

Octal-to-binary conversion is unusually simple compared to converting decimal to binary, and the reason comes down to one relationship: 8 = 2³.

One octal digit can represent 8 possible values (0 through 7). Three binary bits can represent exactly 8 possible values too (000 through 111). Since both ranges match exactly, every octal digit corresponds to precisely one 3-bit binary group — there's no carrying, borrowing, or repeated division involved, just direct substitution.

Decimal doesn't have this property. Because 10 isn't a power of 2, there's no fixed number of bits that lines up evenly with a single decimal digit, which is why converting decimal to binary requires a different method (repeated division by 2) rather than simple digit substitution.

Octal to Binary Conversion Table

Each octal digit has exactly one 3-bit binary equivalent:

Octal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

This table is the entire method. Converting any octal number to binary just means looking up each digit here and joining the results.

How to Convert Octal to Binary Step by Step

1. Write the octal number and confirm every digit is 0-7.
2. Separate the digits so each one is handled individually.
3. Find the 3-bit binary equivalent for each digit using the table above.
4. Join the binary groups together in the same order as the original digits.
5. Remove unnecessary leading zeros from the very front of the combined result, if a normalized (shortest) binary value is wanted.

Example: Convert 157 Octal to Binary

Octal digit:   1     5     7
3-bit group: 001   101   111

Combine: 001 101 111

157₈ = 001101111₂ (grouped)
157₈ = 1101111₂ (normalized)

Checking the result against decimal confirms it: 157₈ = (1 × 64) + (5 × 8) + (7 × 1) = 111₁₀, and 1101111₂ = 64 + 32 + 8 + 4 + 2 + 1 = 111₁₀. Both sides match.

More Octal to Binary Examples

Octal	3-Bit Groups	Binary (Normalized)
7	111	111
10	001 000	1000
17	001 111	1111
52	101 010	101010
100	001 000 000	1000000
345	011 100 101	11100101
725	111 010 101	111010101
1234	001 010 011 100	1010011100

Each row was checked by converting the same octal value straight to decimal and comparing it against the decimal value of the resulting binary — for instance, octal 725 = 469 in decimal, and binary 111010101 also equals 469, confirming the conversion.

If you'd rather not do the digit-by-digit lookup by hand, the Octal to Binary Converter performs the same conversion instantly and shows the 3-bit breakdown for any octal input.

Leading Zeros: What Gets Dropped and What Doesn't

Leading zeros can be a source of confusion because the grouped form and the normalized form of the same number look different. Take octal 5: its 3-bit group is 101, not 000101 — there's no reason to pad a single-digit conversion with extra zero groups that were never part of the number.

For a multi-digit number like 157, the grouped intermediate form is 001 101 111. The leading zeros in that very first group (from the digit 1 → 001) aren't significant to the number's value, so they can be dropped once the groups are joined, leaving 1101111. But zeros that appear in the middle or at the end of a number — like the two zeros in octal 100 → 001 000 000 → 1000000 — must stay, because dropping those would change the value entirely (1000000 is 64, not 1).

The rule is simple: only drop leading zeros from the very front of the final combined result. Never remove zeros from the middle or the end.

Can You Convert Octal to Binary Through Decimal?

Yes. Octal → decimal → binary is a valid alternative: convert the octal number to decimal using powers of 8, then convert that decimal value to binary using repeated division by 2. It produces the same answer, but it takes two conversion steps and a decimal intermediate value instead of one direct lookup. For ordinary octal-to-binary conversion, the 3-bit mapping method above is simpler and less error-prone. If you specifically need the octal-to-decimal step explained, see How to Convert Octal to Decimal. The same 3-bit mapping is also the first step in converting octal to hexadecimal, which regroups those same bits into sets of four — see How to Convert Octal to Hexadecimal for the full method.

Why Binary and Octal Group So Cleanly

The 3-bit relationship works in both directions. Grouping a binary number into sets of 3 bits (counting from the right) and converting each group to its octal digit gives the octal equivalent directly:

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

This is the exact same table as the octal-to-binary table above, just read in the opposite direction — which is why the two conversions are mirror images of each other.

Common Octal to Binary Conversion Mistakes

• Using an invalid octal digit. Octal only has eight digit symbols, 0-7. A digit like 8 or 9 has no 3-bit mapping and was never valid octal to begin with.
• Not using exactly 3 bits per digit. Every octal digit maps to exactly three binary bits, even ones like 1 or 2 that could technically be written with fewer bits (1 instead of 001). Skipping the padding during the digit-by-digit step misaligns every group after it.
• Converting the number as if it were decimal. Octal 52 is not "fifty-two" — treating it with base-10 place values instead of base-8 gives a completely different (and wrong) result.
• Reversing the binary groups. Each 3-bit group must stay in the same left-to-right order as its source octal digit; swapping group order changes the value.
• Dropping zeros that aren't leading. Only the non-significant zeros at the very front of the combined result can be removed — zeros elsewhere in the number are significant and change the value if dropped.
• Confusing octal-to-binary with binary-to-octal. The two conversions use the same table but go in opposite directions — applying the wrong direction gives a result that looks plausible but isn't correct for the number you started with.

Octal to Binary vs Binary to Octal

These two conversions are inverse operations that share the same 3-bit mapping table, just applied in opposite directions:

• Octal to binary: replace each octal digit with its 3-bit binary group, then join the groups.
• Binary to octal: starting from the right, group the binary digits into sets of three, then replace each group with its octal digit.

If you need to go from binary to octal, the Binary to Octal Converter handles the grouping step for you.

How to Check an Octal to Binary Conversion

Two reliable ways to verify a conversion:

• Recheck each digit's group. Walk back through the octal number one digit at a time and confirm each one matches its row in the conversion table above.
• Compare decimal values. Convert both the original octal number and your binary answer to decimal — if they match, the binary conversion is correct. The Octal to Binary Converter shows the decimal and hexadecimal equivalents alongside the binary result, so you can cross-check all three at once.

Frequently Asked Questions

How do you convert octal to binary? Replace each octal digit with its 3-bit binary equivalent, then join the groups together in order. For example, octal 157 converts digit by digit: 1 → 001, 5 → 101, 7 → 111, giving 001101111, which normalizes to 1101111 in binary.

Why does each octal digit equal three binary bits? Octal is base 8, and 8 = 2³. One octal digit can represent 8 possible values (0-7), which is exactly the range that 3 binary bits can represent (000-111). Since the ranges match exactly, each octal digit maps to precisely one 3-bit binary group.

What is the octal-to-binary conversion table? 0 = 000, 1 = 001, 2 = 010, 3 = 011, 4 = 100, 5 = 101, 6 = 110, and 7 = 111. Each row shows the exact 3-bit binary group for that octal digit.

What is 157 octal in binary? 157 (base 8) equals 1101111 in binary: 1 → 001, 5 → 101, 7 → 111, combined as 001101111 and normalized to 1101111.

Can an octal number contain 8 or 9? No. Octal only uses the digits 0 through 7. A number containing an 8 or a 9, such as 189, is not a valid octal value and has no direct 3-bit mapping.

Do I remove leading zeros after converting octal to binary? Only the non-significant leading zeros from the first digit's 3-bit group can be dropped from the final normalized result. Zeros inside or at the end of the number must stay, since removing those would change the value.

Can I convert octal to binary through decimal? Yes — convert octal to decimal first, then decimal to binary. It produces the same result, but for a direct octal-to-binary conversion the 3-bit mapping method is faster and doesn't require an intermediate decimal step.

Is octal base 8 and binary base 2? Yes. Octal is a base-8 number system using digits 0-7, and binary is a base-2 number system using only 0 and 1. Because 8 is 2³, the two systems line up cleanly in groups of 3 bits.