Rotate

Also called: rotation, rotate right, rotate left, ROR, ROL, circular shift, cyclic shift, bit rotation

A shift in which the bit leaving one end re-enters at the other end, so no bit is lost. After n rotations an n-bit value returns to its start.

A rotate (or circular shift) is a shift with the ends joined. The bit that falls off one end comes back in at the other.

Rotate right: every bit moves one place toward Q0, and the old Q0 goes into Q3. 1101 → 1110.
Rotate left: every bit moves one place toward Q3, and the old Q3 goes into Q0. 1101 → 1011.

No information is lost, so rotations are reversible: rotating right by k undoes rotating left by k. After n single-place rotations, an n-bit register is back where it started. Rotating by k places is the same as rotating by k mod n.

In hardware: a shift register with its serial input wired to its own serial output. A shift-right register with SI = Q0 rotates right. A universal shift register does the same with SIR wired to Q0.

Where it is used:

A register that rotates forever, started with a single 1, is a ring counter.
Cryptography and hashing algorithms mix bits with rotations.
Most processors have rotate instructions (ROL and ROR), sometimes with the carry flag included in the loop.

Compare a plain shift, where the bit that leaves is lost and a fixed value (0, or the sign bit) enters.

Worked examples

Example

Rotate left by two

Rotate the 8-bit value 01101001 left by two places.

1.
The top two bits, 01, will wrap round to the right-hand end.
2.
The remaining bits 101001 move up two places.
3.
Result: 101001 followed by 01 = 10100101.
4.
Check: rotating right by two brings back 01101001.

Example

When does the pattern repeat?

A 6-bit register holds 100100 and rotates right at every edge. After how many edges does it first return to 100100?

1.
Edge 1: 010010. Edge 2: 001001. Edge 3: 100100.
2.
It returns after 3 edges, not 6, because the pattern itself repeats every 3 bits.
3.
In general the answer divides n; it is n only when the pattern has no shorter repeat.

Common mistakes

Shifting in a 0 instead of the bit that left. That is a shift, not a rotate.
Rotating the wrong way. Right moves bits toward Q0; left moves them toward Q3.
Assuming every pattern needs exactly n rotations to come back. Patterns with internal repeats come back sooner.

Practice Rotate

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Learn it step by step

Rotate is taught in Registers and Adders and ALUs.

Registers →Adders and ALUs →

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