BIN2OCT in Apple Numbers: Convert Binary to Octal Without Losing Leading Zeroes

Convert a binary (base-2) value into its octal (base-8) representation. Each group of three binary digits corresponds to one octal digit.

One-line example: =BIN2OCT("10011") → 23 (Apple-documented or independently checked expected display). Official Apple BIN2OCT function reference (checked 2026-10-13).

=BIN2OCT(binary-string, convert-length)

binary-string — required, string value: Apple says it must contain only 0 and 1. Treat imported identifiers and bit patterns as text. Its examples use both quoted digit strings and an unquoted numeric literal, but quoting binary makes the intended base unmistakable. Apple BIN2OCT specification.

convert-length — optional, number value: A minimum display width from 1 to 16 inclusive; if omitted, the assumed width is 1. Numbers pads shorter output with zeros on the left. The parameter is not an octal digit count to extract, nor a truncation maximum. Apple BIN2OCT specification.

The return is an octal representation, not a decimal digit count: binary 10011 is decimal 19, displayed as octal 23 because 2 × 8 + 3 = 19.

Formula punctuation and locale: These examples follow Apple’s English function reference, with commas separating arguments. In localized Numbers editions, translated function identifiers and semicolons may apply. For example, Apple’s Portuguese-Brazil article calls BIN2OCT BINPARAOCT and shows semicolons; this is a locale display. Use the function browser in the target Numbers locale rather than mechanically swapping separators. Apple’s localized BIN2OCT help; Apple argument types (checked 2026-10-13).

1. Create a new spreadsheet in Numbers and add a table called Conversions. This guide assumes no special add-ons, scripts or API access.
2. Type the headers shown below into row 1. Set imported code columns to Text before entering strings such as 00101, F, or 3F; otherwise a conversion may silently change the source representation.
3. Enter source examples and formulas in the indicated rows. Each formula references cells in the same table; direct formulas use ordinary A2, B2, C2 syntax. Other tables or sheets need table-qualified references described in Apple’s official cell-reference guide.
4. Read the last column as the expected output, not a native-test report. For padded output keep an output column that preserves the displayed leading zeroes; evaluate actual formatting in Numbers before exporting a production file.

Testing distinction: A mathematical base conversion explains the expected numerical value; it does not prove that a particular Apple Numbers locale treats every source cell as text, preserves padding in an export or accepts values beyond documented limits. Apple’s argument types (checked 2026-10-13).

Example 1. =BIN2OCT("100111",3) → 047. Binary 100111 = 39 decimal = octal 47; requesting three characters adds one leading zero.

Example 2. =BIN2OCT("101101") → 55. Binary 101101 = 32+8+4+1=45 decimal = 5×8+5.

Example 3. =BIN2OCT("00101",4) → 0005. Five decimal retains its value while the display is widened.

Convert a permission bitmask for an octal specification

A six-bit mask such as 110101 represents decimal 53. Its octal counterpart is 65; compute with =BIN2OCT("110101"). This is handy for a system that documents flags as three-bit groups: 110 101 → octal 6 5. The bit pattern and numeric value are unchanged; only notation changes.

Preserve a fixed-width code

If the receiving system expects four octal characters, use =BIN2OCT(A2,4) instead of assuming cell formatting adds the correct zeros. This is a minimum width, so larger results are not shortened. A source 10011 yields expected 0023 with width 4.

Cross-check the arithmetic without a Numbers engine

Group a binary string from right to left in three-bit chunks. For 100111, group 100 111, yielding octal 47. Calculate 4×8+7=39 and verify binary 32+4+2+1=39. This independent check does not establish application-specific negative-number or input-parsing behavior.

Error-code limitation: Apple’s function article documents some inputs as “returns an error” without prescribing a stable literal error label. The table above intentionally says error rather than inventing a specific #VALUE!, #NUM! or implementation-specific diagnostic. If your locale reports something different, inspect Apple’s formula-error guidance and verify the source data type (checked 2026-10-13).

Negative numbers, bounds and implementation limitations

Apple notes that this converter uses two’s-complement notation and that negative values are displayed using 11 octal digits. A leading ASCII minus character in the source is not the way to request that interpretation; Apple demonstrates an error for =BIN2OCT(-101101). The precise input-bit-width/negative threshold is not specified by the excerpted Apple function article. Do not apply Excel’s limits or invent sign-extension tests without native verification.

Copying formulas across sheets

If the original sample cells are stored in Table 2 instead of the same table, a reference can be written using Apple’s documented form Table 2::A2. To refer to a different sheet, a qualified example is Sheet 2::Table 2::A2. Do not assume Excel-style Sheet!A2 notation works in Numbers; use the application’s reference picker and the Apple reference instructions.

BIN2OCT targets base 8 directly from base 2. BIN2DEC instead returns a decimal number; BIN2HEX targets base 16. BASETONUM(A2,2) offers a generic way to get decimal from a binary string, and NUMTOBASE can convert decimal to another base. Do not treat a base-2 string such as 10011 as a decimal input to NUMTOBASE—that changes its meaning. Official definitions: BIN2OCT, BASETONUM, NUMTOBASE.

Application, release and platform compatibility: what is established

This function is present in the current official Apple Formulas and Functions Help, documentation edition 15.4, in the Engineering category. The general help is used with Numbers and related Apple productivity applications. Documentation edition 15.4 is not evidence that the function was introduced in Numbers app version 15.4, nor proof it behaves identically in all older macOS/iOS/iPadOS/iCloud releases. Official help; Numbers for Mac release notes (reviewed 2026-10-13).

Apple’s documented English syntax and example results are the evidence for these claims. This guide does not establish parity with Microsoft Excel, Google Sheets, LibreOffice, or browser-based spreadsheet tools: those products have independent error codes, limits, coercion rules, localization and negative-number encodings. Their behavior is not used as Apple Numbers evidence.

Precision and display policy

Base conversion is exact arithmetic only while the input can be represented and parsed accurately. The official individual function documentation does not specify a universal maximum exact integer magnitude, rounding or overflow policy for all possible inputs, so this guide deliberately avoids such thresholds. Treat long codes or signed values as data requiring native app checks. A width parameter adds zeros for presentation; it does not increase information in the underlying number.

Does this formula need an extension, macro or paid service? No. It is documented by Apple as a built-in spreadsheet function. No external API is required for the examples here.

Can I use a cell reference instead of typing an argument? Yes; the reproducible worksheet uses A2 and, where relevant, B2/C2. Refer to Apple’s Numbers-specific table scope syntax when using another table or sheet.

Are the displayed results verified in the Apple Numbers app? No. Apple-published examples were documentation-checked, and positive-number examples were independently computed. Native execution and formatting/export screenshots were not performed.

• Apple official reference — Syntax, allowed digits, 1–16 width/default, zero-padding, signed two’s complement, 4 published examples.
• Apple official reference — String versus numeric argument definitions.
• Apple official reference — Cross-table and cross-sheet reference notation.
• Apple official reference — Portuguese-Brazil localization of BIN2OCT as BINPARAOCT and semicolon separators.
• Apple formula-error troubleshooting — diagnosing invalid formulas and references.
• Numbers for Mac release documentation — release context only; not a function-specific introduction date. Method: Manual comparison of Apple’s official help with independent Python exact-integer base arithmetic for positive examples, on 2026-10-13 UTC. Zero native Numbers execution. Unresolved native-behavior questions are identified explicitly in this guide.