BITLSHIFT in Apple Numbers: Shift Binary Values Left, With Examples

=BITLSHIFT(12,3) → 96 (Apple’s published example). Binary 1100 becomes 1100000 after shifting three places left. Official Apple BITLSHIFT reference (checked 2026-10-13).

BITLSHIFT moves the binary representation of a nonnegative number left by the specified count of positions and returns the result as a number. For small, exact whole-number examples this is the same arithmetic as multiplying by a power of two; that identity is a useful independent check, not a claim about undocumented precision limits. Apple’s documented purpose.

=BITLSHIFT(value, shift-amount)

• value (required): The numeric value whose binary bits are shifted. Apple explicitly states that value must be nonnegative. Apple does not publish a specific maximum bit width on this article; do not assume Excel’s or another program’s limits apply. Apple BITLSHIFT definition.
• shift-amount (required): How many positions to move the bits left. Position count comes second, so BITLSHIFT(3,12) is not interchangeable with BITLSHIFT(12,3). The Apple help does not specify a default; the examples always supply both arguments. Apple BITLSHIFT definition.
• Return: A numeric result, rather than a string of ones and zeroes. Apple describes the result as a number. Apple BITLSHIFT definition.

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 =BITLSHIFT(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 =BITLSHIFT(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.

For Apple’s exact example, the nonnegative integer 12 is binary 1100. Moving its bits three positions left adds three low-order zeros (1100000). The latter bit pattern is 64+32=96. Equivalently, the independent mathematical check is 12 × 2³ = 96. The function returns 96 as a number, not the text 1100000. This observed output is Apple’s published example, not a screenshot produced here. Apple BITLSHIFT example.

For the 5,1 row, binary 101 shifted left gives 1010, which is decimal 10. For 13,0, moving no positions leaves 13 mathematically; Apple does not provide this exact example on the page, so it is explicitly an independently predicted check. Each row uses only small nonnegative whole numbers.

Use case 1: Construct a bit-mask for a selected flag

Suppose the Flag positions table contains B2 = 4, meaning the fifth position from the right when the rightmost position is numbered zero. Enter =BITLSHIFT(1,B2). Independently, one shifted four places left is binary 10000, decimal 16. Use this where a system stores several on/off options in one integer. The number is a mask, not a formatted binary string.

For a second example, if B3 = 0, =BITLSHIFT(1,B3) mathematically returns 1. This also illustrates that shift counts and flag positions should be consistently zero-based in a data model you control; the function documentation does not define your application’s flag numbering.

Use case 2: Calculate powers-of-two weights without typing them repeatedly

If the Weights table lists small nonnegative integer bit positions in column A, put =BITLSHIFT(1,A2) in B2 and fill down. With A2:A6 holding 0, 1, 2, 3, 4, the independent expected numeric results are 1, 2, 4, 8, 16. For those inputs, the ordinary arithmetic control =POWER(2,A2) has the same numerical result, but that does not certify identical overflow, type coercion or error behavior for other inputs.

Use case 3: Interpret a packed integer using another documented bitwise function

For a packed integer 13 (1101 in binary), position 2 (zero-based), the third bit from the right, has weight 4. The mathematical calculation BITAND(13,BITLSHIFT(1,2)) is 4, showing that this flag is present. When constructing this in Numbers, use =BITAND(13,BITLSHIFT(1,2)); the nested combination is an independently reasoned expected result, not a native Numbers test. Apple’s official BITAND and BITLSHIFT entries appear together under Engineering functions.

Use case 4: Cross-table inputs

In a table named Shift Results, refer to a separate table’s input cell with a qualifier such as =BITLSHIFT(Inputs::A2,Inputs::B2) when Inputs contains the two values. Apple’s cell-reference guide demonstrates the Table 2::B5 style; typing or selecting actual cells through the Numbers formula editor prevents misspelled table names. Apple cell reference rules.

What the official article does not establish

Apple’s short BITLSHIFT page documents the positive-direction shift and that value is nonnegative. It does not state a universally safe largest integer, largest shift, handling for fractional counts, or the native error text for each out-of-domain input. Those questions are not answered by independent Python bitwise calculations; leave them for Numbers-on-device verification. The independent examples use exact, deliberately small integers to avoid suggesting a certified implementation width.

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: BITLSHIFT 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 BITRSHIFT — moves nonnegative numbers right rather than left, helpful for reversing an illustrative shift when high-order precision is not lost.
• Apple function catalogue — Engineering functions list BITAND, BITOR, BITXOR and BITLSHIFT separately. BITAND combines masks; it is not an alias for BITLSHIFT.
• Apple reference guidance — table-qualified inputs when a mask position is stored separately.

Is BITLSHIFT the same as multiplying by two? For small whole-number inputs, shifting left by one bit corresponds arithmetically to multiplying by 2; moving left k positions corresponds to multiplying by 2^k. Treat this as a mathematical identity for the samples, not a universal guarantee about Numbers numeric precision.

Can I pass a negative number? Apple explicitly says that value must be nonnegative. Negative-value behavior is therefore outside the documented supported input set.

Is =BITLSHIFT(12,3) supposed to return text 1100000? No. Apple says it returns 96. The bit string explains the calculation; the function result is numeric.

Does this work in old Numbers versions? The function appears in Apple Functions Help 15.4. The original introduction version has not been independently established for this guide; only claim availability after platform-specific testing.

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

• Function purpose, precise signature, required argument order, special documented constraints and official example: Apple BITLSHIFT 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.