Bitwise Calculator

Compute AND, OR, XOR, NOT, and bit-shift operations with binary and hex output.

Bitwise operations, explained

Bitwise operators work directly on the binary representation of integers. AND keeps only bits that are 1 in both operands, OR keeps any bit set in either, and XOR keeps bits set in exactly one operand. NOT flips every bit (32-bit signed result in JavaScript). Left shift multiplies by powers of 2; right shift divides. These are fundamental to flags, masks, and low-level algorithms.

Related tools: decimal to binary converter, base converter, and the decimal to hex converter.

Built and maintained by Meet Shah · Last updated 1 August 2026

What this tool is used for

Checking the result of a mask operation against what you expected.
Working out which flags a combined value has set.
Verifying a shift's result at a specific width.
Building a mask from individual bit positions.
Confirming an implementation's bitwise logic.

Frequently Asked Questions

Why are the results 32-bit?: Because JavaScript's bitwise operators convert their operands to signed 32-bit integers, and so does this. A value above 2³¹−1 wraps to negative, and anything above 2³² is truncated outright — which is why 1 << 31 is −2147483648 rather than a large positive number.
What is the difference between >> and >>>?: Sign handling. `>>` is an arithmetic shift that copies the sign bit inwards, so −8 >> 1 is −4. `>>>` is a logical shift that fills with zeros, so −8 >>> 1 is 2147483644. Using the wrong one on a value that might be negative is a classic source of impossible-looking numbers.
How do bit flags work?: Each option is one bit, so they combine with OR and are tested with AND: `flags | WRITE` sets it, `flags & WRITE` checks it, and `flags & ~WRITE` clears it. Eight independent booleans then fit in a single byte, which is why file permissions and protocol headers are built this way.
Is shifting really faster than multiplying?: It was, decades ago. Any compiler today turns `x * 2` into a shift when that is faster, and on modern CPUs multiplication is a few cycles anyway. Write the arithmetic you mean — `x << 3` for "times eight" is a micro-optimisation that costs the next reader real time.
What is XOR good for?: Toggling and difference. `x ^ mask` flips exactly the bits set in the mask, and `a ^ b` is zero only when the values are equal — which is why it appears in checksums, in simple ciphers, and in the trick for finding the one unpaired value in a list.

Common errors and gotchas

Not fixing the width, which makes NOT and right-shift results undefined.
Confusing arithmetic and logical right shift, which differ for negative values.
Shifting by more than the width, which is undefined behaviour in several languages.
Assuming JavaScript's bitwise operators are 64-bit, when they coerce to 32.
Reading a negative result as an error rather than two's complement.