OCT2BIN in Apple Numbers: Convert Octal Digits to Binary

OCT2BIN changes an octal (base-8) representation into binary (base 2). Each octal digit corresponds mathematically to three binary bits: 7 ↔ 111, 5 ↔ 101 and 0 ↔ 000. The function is practical for understanding permissions masks, grouped bit fields and data-system notation.

Example: =OCT2BIN(127,8) → 01010111 (Apple’s documented expected display; not a native test). Apple official OCT2BIN help, v15.4 (checked 2026-10-13).

=OCT2BIN(octal-string, convert-length)

octal-string (required, string): Apple accepts octal representations made of digits 0 through 7 only. Its examples also show unquoted numeric literals. Quoted strings or cells explicitly formatted as text avoid ambiguity when the input has leading zeros. The minus sign is explicitly prohibited for this function.

convert-length (optional, number): minimum output length 1 through 32, default 1. If the binary output needs fewer places, Numbers pads zeros at the beginning; if it already needs more digits, the width does not truncate it.

Argument order matters: the source value or string goes first; the optional minimum displayed width goes second. Apple’s help uses commas in these English examples. The width argument is optional; do not include an empty comma if you are using the default. Apple OCT2BIN definition (checked 2026-10-13).

What counts as a valid source string?

Apple’s engineering function article governs this function specifically, rather than Excel’s rules. In the example worksheets, source entries are explicitly Text. Do not assume that a numeral copied from a PDF is automatically the same representation as a text value after parsing. If a workbook uses a locale-specific argument separator, insert the function from Numbers’ function browser and follow the local syntax instead of blindly copying the English comma. Apple argument types; Apple cell references (checked 2026-10-13).

1. In a new Numbers spreadsheet, add a table named Conversions (you can keep the default name). Put Source as text in A1, Formula in B1 and Expected display in C1.
2. Format column A as Text before entering the source digits. Copy the values in the second column of the following table into A2 onward. The source is not a spreadsheet formula.
3. In B2 onward, enter each displayed formula below. A Numbers cell should contain the formula, not its literal string representation. Compare the displayed answer to C’s expected value.
4. Where a value includes leading zeros, inspect the destination cell’s display formatting; retain the source and output as text when exporting identification strings. This test plan was authored but not run natively.

The expected results were checked using independent integer-base conversion. Apple-published examples are called out separately below. Do not treat this as a native Numbers test log. Apple OCT2BIN article (checked 2026-10-13).

Apple’s directly documented examples

Reading three-bit permissions groups

For text value 755 in A5, the expected =OCT2BIN(A5,9) is 111101101. Split that display into groups 111 | 101 | 101: each group matches one octal digit (7 | 5 | 5). This makes it easier to inspect flag patterns. It does not grant, check, or change any computer permission; it only transforms the number representation.

Comparing octal and hexadecimal representations

The same octal 377 has binary 11111111 and hexadecimal FF. =OCT2BIN("377") and =OCT2HEX("377") are two independent representations of decimal 255. This is a useful verification pattern for register dumps: convert the value two ways and verify against base arithmetic, rather than reading converted strings as decimal numerals.

Fixed-length binary data

=OCT2BIN("127",8) should display 01010111 per Apple. It preserves an eight-place presentation but does not mean there is an extra significant high bit; the leading 0 is padding. When exporting an ID or bit string, treat it as text so display padding does not disappear.

Multi-row conversion table

Format the source column as Text, put octal inputs in A2:A7, and fill =OCT2BIN(A2,9) down a destination column for a consistent minimum nine places. Apple documents the argument width, but the formula fill-down and text-export behaviour were not native tested in this research.

When not to use OCT2BIN: OCT2BIN is particularly useful for bit-mask auditing, teaching number systems, and hardware descriptions. It should not replace specialized validation for very large binary data because the cited Apple article does not establish every input-magnitude limit.

Limit of this research: Apple documents parameter types, width ranges and certain invalid characters. It does not supply a complete test matrix in the cited function article for blanks, decimals, very large values, regional parsing, and coercion of every cell type. Thus this guide neither invents exact error codes nor claims unsupported interoperability behaviour. Apple OCT2BIN help; Apple official formula-error review guidance (checked 2026-10-13).

Apple’s Formulas and Functions Help 15.4 contains an entry for OCT2BIN and the argument order and limits stated above. Apple’s current Numbers for Mac User Guide identifies version 15.4, and its Mac release history describes features in that release. Apple also documents Numbers 15.4 for iPhone in its iPhone release history. Those release pages establish software/documentation version context; they do not constitute a test of the function on Mac, iPad, iPhone, or Numbers for iCloud. The function browser, locale and availability on each older release remain not independently verified. Mac guide; Apple 15.4 function article (checked 2026-10-13).

Excel, Google Sheets, LibreOffice and other spreadsheets may provide similarly named engineering functions with different width limits, signed-number conventions, string coercion or errors. This guide makes no cross-product parity claim because no external spreadsheet execution was used as Numbers evidence. If transferring an Excel file, verify the formulas and output in Numbers itself before relying on critical reports.

Locale and table-reference guidance

For English-language Numbers help the argument separator shown is a comma. Locale settings can affect punctuation and decimal separators; do not infer your installed syntax from English screenshots. Apple recommends referencing cells in tables using the formula editor; when a source is on a separate sheet/table, select that cell to insert the proper reference rather than typing an unverified table qualifier. Apple argument types; Apple table references (checked 2026-10-13).

The related functions below belong to Apple’s official Engineering catalogue. All are linked to Apple’s real, version-specific help pages, for readers who want to compare the specifications:

• DEC2OCT: official Apple Functions Help 15.4 — neighbouring base-conversion direction.
• OCT2DEC: official Apple Functions Help 15.4 — neighbouring base-conversion direction.
• OCT2HEX: official Apple Functions Help 15.4 — neighbouring base-conversion direction.

Apple’s function category catalogue lists these functions. Checked on 2026-10-13.

Are octal 10 and decimal 10 equal?

No. Octal 10 equals decimal 8, so the corresponding binary is 1000.

Why did 127 become 01010111?

Octal 127 represents decimal 87, binary 1010111, then Apple pads to eight characters.

Does this accept negative octal?

No. Apple explicitly says a minus sign is prohibited for OCT2BIN.

• [S1] Function identity, signature, accepted digits/strings, optional width and Apple examples: Apple OCT2BIN — Formulas and Functions Help 15.4 (accessed 2026-10-13 UTC). Claims in the syntax, example, and troubleshooting sections derive from this page.
• [S2] Cell and argument types: Apple Types of arguments and values and Refer to cells in formulas (accessed 2026-10-13 UTC). These support table/argument terminology, not application execution.
• [S3] Catalogue and versions: Apple function catalogue, Numbers for Mac 15.4 user guide and Mac version history (accessed 2026-10-13 UTC). These support the official current documentation/release identification, not full historical availability.
• [S4] Mathematics: examples were independently evaluated via integer-base arithmetic on 2026-10-13; this is not a Numbers computation.
• [S5] Native Apple Numbers execution, screenshots, import/export and cross-device behavior: Not tested.