Binary Alignment Tool

Power of Two Alignment Calculator

Align a nonnegative integer to a power-of-two boundary such as 8, 16, 64, 256, or 4096. Calculate aligned-down and aligned-up values, padding, remainder, mask, and binary results.

Align up & down Exact BigInt math Power-of-two mask

Align an Integer to a 2ⁿ Boundary

Value Nonnegative integer

Input format

Alignment Must be power of 2

Example: value 1000 with alignment 64 → down 960, up 1024.

Aligned Down 960 Largest multiple of 64 ≤ 1000

Aligned Up 1024 Smallest multiple of 64 ≥ 1000

Remainder 40

Padding Up 24

Alignment Mask 63

Exponent 6

Aligned down binary

1111000000

Aligned up binary

10000000000

Binary Boundary

What Is Power-of-Two Alignment?

Power-of-two alignment places an integer on a boundary that is an exact multiple of a power of two such as 2, 4, 8, 16, 32, 64, 256, or 4096.

Alignment is widely used in computing because powers of two map naturally to binary bit positions. A value aligned to 64, for example, must be an exact multiple of 64.

This calculator shows both directions: the aligned-down value is the greatest aligned boundary not above the input, while the aligned-up value is the smallest aligned boundary not below it.

Power-of-two alignment alignment = 2^n

How to Use

How to Use the Power of Two Alignment Calculator

Enter the integer value Type the nonnegative value you want to align.

Select decimal or binary input The value can be supplied in decimal or binary form.

Enter the alignment Use a positive power of two such as 8, 16, 64, 256, 1024, or 4096.

Calculate both boundaries The result shows aligned down, aligned up, remainder, padding, mask, exponent, and binary forms.

Worked Example

Align 1000 to a 64-Byte Boundary

A 64-byte alignment means valid boundaries occur at multiples of 64: 0, 64, 128, 192, and so on.

1000 aligned to 64

Value = 1000 Alignment = 64 1000 ÷ 64 = 15 remainder 40 Aligned down: 15 × 64 = 960 Aligned up: 16 × 64 = 1024 Padding required: 1024 – 1000 = 24 Result: Down = 960 Up = 1024

Align Down

How Alignment Down Works

Aligning down removes the remainder after division by the alignment. The result is therefore the largest exact multiple that does not exceed the original value.

General integer formula alignDown(x,a) = floor(x / a) × a

For 1000 aligned to 64, the quotient is 15 with remainder 40. Multiplying 15 by 64 gives the aligned-down value 960.

Align Up

How Alignment Up Works

Alignment up returns the smallest multiple of the alignment that is at least as large as the input.

General formula alignUp(x,a) = ceil(x / a) × a

If the input is already aligned, no padding is required and the aligned-up value equals the original value.

Bitwise Method

Power-of-Two Alignment with Bit Masks

Power-of-two alignments allow especially efficient bitwise formulas. If a is a power of two, then a − 1 produces a mask containing ones in every bit below the alignment boundary.

Alignment mask mask = a – 1

For alignment 64, the mask is 63. In binary, 64 is 1000000 and 63 is 111111.

Bitwise alignment formulas

mask = alignment – 1 align down: x & ~mask align up: (x + mask) & ~mask Valid when alignment is a positive power of two.

Alignment Check

How to Check Whether a Value Is Already Aligned

A value is already aligned when its remainder after division by the alignment is zero.

Alignment test x mod a = 0

With a power-of-two alignment, the equivalent bitwise check is (x & (a − 1)) = 0.

For example, 1024 is aligned to 64 because 1024 is exactly 16 × 64. Its padding-up requirement is therefore zero.

Reference

Common Power-of-Two Alignment Examples

Value	Alignment	Aligned Down	Aligned Up	Padding Up
15	8	8	16	1
16	8	16	16	0
100	16	96	112	12
1000	64	960	1024	24
1024	64	1024	1024	0
4097	4096	4096	8192	4095

Valid Alignments

Why Must the Alignment Be a Power of Two?

General integer alignment can use any positive divisor, but this calculator specifically focuses on power-of-two boundaries because they are important in low-level computing and support clean bit-mask operations.

Examples of valid alignments include 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, and larger powers of two.

Values such as 3, 6, 10, 12, or 100 are not valid power-of-two alignments.

Memory

Power-of-Two Alignment in Memory and Systems Programming

Memory alignment is one of the most common uses of power-of-two boundaries. Data structures, memory blocks, pages, SIMD data, and hardware interfaces may require or benefit from particular alignment constraints.

For example, a structure that must begin on a 16-byte boundary can start at addresses such as 0, 16, 32, 48, 64, and 80, but not at 70.

When an address or offset is not aligned, the align-up operation finds the next valid boundary while align-down finds the preceding one.

Padding

What Is Alignment Padding?

Padding is the number of units that must be added to reach the next aligned boundary.

Padding up padding = alignUp(x,a) – x

For 1000 aligned to 64, the next boundary is 1024, so the required padding is 24.

If the value is already aligned, padding equals zero.

Remainder

Alignment Remainder and Offset Within a Block

The remainder tells you how far the current value is from the preceding aligned boundary.

Remainder remainder = x mod alignment

In the 1000-to-64 example, the remainder is 40. This means 1000 is 40 units past the aligned boundary at 960.

Applications

Where Power-of-Two Alignment Is Used

Memory Addresses

Move an address or offset to the required hardware or ABI boundary.

Memory Allocation

Calculate aligned blocks and padding when arranging memory layouts.

File Offsets

Place data on sector, block, or format-specific boundaries.

Page Boundaries

Work with common page-size boundaries such as 4096 bytes.

Buffers

Round offsets and capacities to binary-friendly boundaries where required.

Low-Level Code

Verify bit-mask formulas used in kernels, drivers, runtimes, and embedded code.

Common Mistakes

Common Power-of-Two Alignment Mistakes

Using an alignment that is not a power of two

Bit-mask alignment formulas require a positive power-of-two alignment. This calculator rejects values such as 10 or 12.

Always adding one full alignment

If a value is already aligned, align-up should return the value itself, not the next boundary.

Confusing alignment with next power of two

These are different operations. Aligning 70 to 16 gives 80, while the next power of two for 70 is 128.

Confusing remainder and padding

Remainder is the distance from the previous boundary. Padding is the distance to the next boundary.

Applying fixed-width bitwise assumptions to huge integers

This calculator uses BigInt arithmetic so it is not restricted to 32-bit JavaScript bitwise integers.

FAQ

Power of Two Alignment Calculator FAQs

It means placing a value on a boundary that is an exact multiple of a power of two such as 8, 16, 64, or 4096.

The next multiple of 64 after 1000 is 1024, so the aligned-up result is 1024.

The greatest multiple of 64 below 1000 is 960, so the aligned-down result is 960.

Both align-down and align-up return the original value, and required padding is zero.

For a power-of-two alignment a, the alignment mask is a − 1. For alignment 64, the mask is 63.

A value is aligned when its remainder modulo the alignment is zero.

Yes. One is 2⁰, so it is technically a power-of-two alignment. Every integer is aligned to 1.

No for this calculator. Twelve is not a power of two. Use values such as 8, 16, 32, or 64.

No. Alignment rounds to a multiple of a chosen boundary, while a next-power calculation changes the value to a power of two itself.

It is the amount that must be added to the input to reach the next aligned boundary.

Yes. Select Binary as the value format and enter the bit pattern directly. The alignment itself is entered as a decimal power of two.

Yes. The calculation uses JavaScript BigInt so it is not limited to 32-bit integer ranges.