BITRSHIFT in Apple Numbers: Shift Binary Values Right and Extract Flags

=BITRSHIFT(12,3) → 1 (Apple’s published example). Binary 1100 loses three rightmost digits and becomes binary 1. Official Apple BITRSHIFT reference (checked 2026-10-13).

BITRSHIFT shifts the binary representation of a nonnegative number right by a given number of positions. Apple specifically states that a right shift removes digits from the rightmost side of the binary representation. For small nonnegative integer examples, an independent check is to divide by a power of two and discard the fractional part. Apple’s documented purpose.

=BITRSHIFT(value, shift-amount)

• value (required): Number whose bits are shifted. Apple explicitly requires a nonnegative input. Its function article does not certify a particular integer bit width or signed representation. Apple BITRSHIFT definition and note.
• shift-amount (required): Number of positions to shift right. It is the second argument; reversing the arguments changes the calculation. Apple does not describe an omitted-argument default. Apple BITRSHIFT definition.
• Return: Number left after removing low-order bits. The output is decimal-number display, not a textual binary representation. Apple BITRSHIFT example.

Required/default summary: Both arguments are shown as required in Apple’s two-argument signature. Its article names no optional arguments or defaults. The formula examples therefore supply exactly two values, in the documented order. This is an English function identifier, not evidence that a translated locale uses the same identifier. Official function page.

1. Create a new Numbers document with a single table named Inputs. Put the header labels in row 1. Use the A column for the first argument, B for the second, C for the formula and D for the expected output if you want an independent comparison. The table below gives actual rows and their mathematically expected outputs.
2. Type each row’s numeric data into A and B as ordinary numeric cell values, not quoted text. In C2 enter =BITRSHIFT(A2,B2). Copy the formula down; the row-relative references should advance from 2 to 3, and so forth. Follow Apple’s formula and cell reference guidance for copied, moved and cross-table references.
3. Compare what Numbers displays against the Expected column. The expected figures here were derived independently or were published by Apple. No native spreadsheet execution occurred for this guide.
4. To isolate an error, start with the documented literal example =BITRSHIFT(12,3) before introducing table references; this separates cell-reference mistakes from the function’s essential behavior.

Inputs and expected outputs

Important: The table is a reproducible test plan and does not claim that a real Numbers workbook has been opened. Row labels and binary annotations are explanatory text; formulas return values, not explanatory annotations.

Apple begins with 12 (1100 in binary). Right-shifting three positions removes the rightmost three digits, leaving 1. That is decimal 1. This is Apple’s own result, independently checked by integer arithmetic 12 // 8 = 1. Apple BITRSHIFT example and note.

With 13 (1101) shifted one place right, the final bit is dropped, leaving 110 = 6; the fractional part of 13/2 is discarded when reasoning about nonnegative integers. With 255 (11111111) shifted four places, the low four digits drop, leaving 1111 = 15. These latter cases are independently computed expected values, not additional Apple-published examples.

Use case 1: Extract a high-order portion of a packed value

Suppose a Packets table has a packed nonnegative integer A2 = 255 and a number of low bits to remove B2 = 4. Put =BITRSHIFT(A2,B2) in C2. The independent expected result is 15 because 11111111 becomes 1111. This technique is useful for integer-coded settings when the intended bit layout is documented by the system that generated the numbers.

Use case 2: Read one flag from a position

For a compact integer 13 (binary 1101), bit position 2 (the third bit from the right, zero-based) is 1. Shift two places right, then isolate the least significant bit with a bitwise AND:

=BITAND(BITRSHIFT(13,2),1)

Independent computation: 13 >> 2 = 3 (11 in binary), and 3 AND 1 = 1, so this flag is on. This is an illustrative nested formula with an independently computed expected result, not an execution transcript from Numbers. Consult Apple’s separate BITAND documentation for its supported input types.

Use case 3: Calculate whole-number groups from a counter

For small nonnegative integer counters, a shift by 1 has the same arithmetic outcome as floor(value/2). Using A2=13, the expected result of =BITRSHIFT(A2,1) is 6, whereas A2/2 is 6.5. The discarded digit is the remainder’s contribution; do not use ordinary rounding when comparing. This is not evidence about fractional input coercion or machine integer limits.

Use case 4: Cross-table references

Place packed values in Inputs::A2 and counts in Inputs::B2, and use =BITRSHIFT(Inputs::A2,Inputs::B2) in the destination table. Apple documents table-qualified references such as Table 2::B5; confirm the actual table name by clicking cells in the formula editor. Apple table reference syntax.

What the official article does not establish

The English Apple documentation confirms a nonnegative value, a rightward position count, and removal of low-order digits. It does not specify maximum safe shift count, maximum supported integer magnitude, treatment of fractional counts, or native error text for every invalid value. Those remain native-test-pending. The examples use exact, limited-width arithmetic only as independent educational checks; they must not be read as an Apple platform certification.

If Numbers displays an error triangle or unexpected value, Apple’s official formula errors and best practices guide explains how to inspect and edit formulas. This research does not fabricate native diagnostic/error codes.

The syntax and examples in this guide use English-language Apple documentation and a comma between function arguments. An installation set to another language/region may localize function names or display different separators. Verify the localized Function Browser rather than generating a different English function URL for each translated name. Decimal punctuation is also locale-sensitive. All test inputs here are plain whole numbers, so they avoid ambiguous decimal separators. Apple function documentation; Apple argument types.

When using more than one table, qualify references by selecting the appropriate source table’s cells in the formula editor. Apple illustrates references in the form Table 2::B5, and the sheet-qualified form Sheet 2::Table 2::B5. Apple’s cell reference rules.

Documented: BITRSHIFT is present in Apple’s public English Formulas and Functions Help, documentation edition 15.4, checked 2026-10-13 (UTC). Apple presents the functions guide for supported Numbers environments, including Mac, iPhone/iPad and iCloud; the help edition alone does not prove execution on every version or device. The date Apple introduced this exact function has not been verified here. Consult Apple’s help overview and Apple’s current Mac release notes and iPhone release notes before making a platform-specific claim.

Not certified: Exact error text, numerical overflow/big-integer limits, text-to-number coercion, type handling or alias behavior from Excel, Google Sheets, or other spreadsheet software. A similarly named function there is not an Apple Numbers test. Import a sample workbook and compare outputs in both environments when compatibility is important. This guide’s arithmetic model is independent of app execution.

• Apple BITLSHIFT — shifts left, whereas BITRSHIFT removes rightmost digits.
• Apple Engineering functions catalogue — BITAND, BITOR and BITXOR are separate bitwise operations used with flags.
• Apple formula-error guidance — diagnosing problematic references and argument entry.

Does shifting right round a fraction? With supported nonnegative whole-number sample inputs, it discards low-order bits, so arithmetic agrees with floor division by a power of two. The function reference does not establish rules for fractional source values.

What is =BITRSHIFT(12,3)? Apple explicitly gives 1: binary 1100 loses three rightmost digits.

Can it shift negative values using the sign bit? Apple’s documented source value must be nonnegative; it is inappropriate to assume a particular signed two’s-complement implementation here.

Does it return TRUE/FALSE? No. BITRSHIFT returns a number; you can separately compare that result to a threshold or inspect a bit to derive a condition.

Claim-level references (official Apple; checked 2026-10-13, UTC):

• Function purpose, precise signature, required argument order, special documented constraints and official example: Apple BITRSHIFT function page.
• Reference notation and cross-table syntax: Apple — Refer to cells in formulas.
• General error troubleshooting: Apple — Review formula errors and best practices.
• Value/type distinctions: Apple — Types of arguments and values.
• Availability scope and version caveats: Apple Formulas and Functions Help overview, Numbers Mac release history, Numbers iPhone release history.

Validation performed: Official documentation checked; independent calculation predictions produced for the explicit sample inputs; each expected number matched the independently calculated model. Validation not performed: opening Numbers, executing formulas in macOS/iOS/iPadOS/iCloud, testing error messages, taking screenshots.