What is the difference between logical and arithmetic right shift?

A logical right shift fills the vacated high bits with zeros, treating the value as unsigned. An arithmetic right shift replicates the sign bit, preserving the sign of a two's-complement number so negatives stay negative.

Does left-shifting multiply by a power of two?

Yes, within the width. Shifting left by n multiplies the value by 2 to the power n, but any bits pushed past the most significant bit are discarded (overflow), which the width masking reproduces.

Why does the width matter for shifts?

Left shifts can push bits out of an 8-bit register that would survive in a 32-bit one, and arithmetic right shift needs to know which bit is the sign bit. Setting the width models real fixed-size hardware behaviour.

Is a right shift the same as integer division?

A logical right shift by n equals unsigned division by 2^n. An arithmetic right shift rounds toward negative infinity, so for negative numbers it differs from the round-toward-zero division most languages use with the / operator.

Is this tool private?

Yes. All shifts are computed locally with exact BigInt arithmetic, so 64-bit values are precise and nothing is transmitted.

Bit Shift Calculator

A bit shift moves all the bits of a value left or right by a number of positions. Shifts are among the fastest CPU operations and underpin fast multiplication and division by powers of two, bit packing, and hash functions. This calculator supports all three common shift modes at fixed register widths.

How it works

Within a register of width bits (mask = (1 << width) - 1):

Left shift (<<) — every bit moves toward the most significant end; zeros enter from the right and bits that fall off the top are discarded. This multiplies by 2^n modulo the width.
Logical right shift (>>>) — bits move toward the least significant end; zeros enter from the left. This is unsigned division by 2^n.
Arithmetic right shift (>>) — like the logical shift, but the sign bit is copied into the vacated high bits, preserving the sign of a two’s-complement value.

Example

Take the 8-bit value 0b00010110 (22):

Left shift by 2 → 0b01011000 = 88 (which is 22 × 4).
Logical right shift by 1 → 0b00001011 = 11.

Now take 0b10110110 interpreted as signed (−74). An arithmetic right shift by 1 gives 0b11011011 (−37), keeping the value negative, whereas a logical right shift would give 0b01011011 (91), changing the sign.

Notes

Choose the width to match your target type. Note that arithmetic right shift rounds toward negative infinity, so -1 >> 1 stays -1, unlike integer division which would round toward zero — a subtle but important difference when implementing signed math with shifts.