Bit Rotate Calculator (Circular Shift)
Perform a circular bit rotation (barrel shift) of an integer left or right within an 8, 16, 32, or 64-bit register.
bits
Direction
Bit width
- 1
Effective rotate amount
3 mod 8 = 3 - 2
Rotate left
(210 << 3) | (210 >> (8 − 3)) = 150Bits leaving one end reappear at the other; result masked to 8 bits.
How does this calculator work?
A bit rotate, or circular shift, moves every bit of an integer left or right by k positions inside a w-bit register, wrapping bits off one end back onto the other. Reduce k by k mod w, then OR the shifted value with the wrapped bits and mask to w bits. Output appears in decimal, binary, and hex.
Formula
How this is calculated
A rotation (also called a circular or barrel shift) moves every bit of the value n by k positions inside a register of fixed width w. Unlike a plain shift, bits pushed off one end are not discarded — they re-enter at the opposite end, so the total number of set bits never changes. Choose the width (8, 16, 32, or 64) that matches the register you are modelling; n must be non-negative and fit within that width.
The calculator first reduces the rotate amount with k mod w, because rotating by the full width returns the original value. A rotate left combines (n << k) with the bits that wrapped around, (n >> (w − k)), then masks the result with (1 << w) − 1 to keep only the low w bits. A rotate right is the mirror image, using (n >> k) and (n << (w − k)). All arithmetic is done with arbitrary-precision integers (BigInt) so 64-bit values stay exact.
The output is shown in decimal, as a zero-padded w-bit binary string, and in hexadecimal padded to the register width. Edge cases: a rotate amount that is a multiple of w leaves the value unchanged, and a value that does not fit in the selected width is rejected. Bit indices in the breakdown are labelled with the most significant bit on the left.
Frequently asked questions
A logical shift discards the bits that fall off the end and fills the vacated positions with zeros. A rotate (circular shift) feeds those bits back in at the other end, so no information is lost and the population count stays the same.
Rotating w times in a w-bit register returns every bit to its original position. The calculator applies k mod w, so a rotate of 8 in an 8-bit register, or 16, 24, and so on, is equivalent to rotating by 0.
The value must be representable in w bits (between 0 and 2^w − 1). If n is larger, widen the register or reduce n; the calculator will not silently truncate it.
Also known as
TG we-Calculate Editorial Team. (2026). Bit Rotate Calculator (Circular Shift) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bit-rotate-calculator
TG we-Calculate Editorial Team. "Bit Rotate Calculator (Circular Shift)." TG we-Calculate. 2026. https://we-calculate.com/calculator/bit-rotate-calculator.
TG we-Calculate Editorial Team, "Bit Rotate Calculator (Circular Shift)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bit-rotate-calculator
@misc{wecalculate_bit_rotate_calculator, title = {Bit Rotate Calculator (Circular Shift)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bit-rotate-calculator}}, year = {2026}, note = {TG we-Calculate} }
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