Another form of shift is the circular shift or bit rotation.

If necessary, circular shift functions can be defined (here in C):

However, not all n-tuples have n distinct circular shifts.

More complex operations such as circular shift (swap being a special case), and certain classes of random number generation also belong here.

Some computers provide both logical and circular shifts, together with the appropriate arithmetic shifts.

Cyclic permutations of definition type 1 are also called rotations, or circular shifts.

Circular shifts are used often in cryptography in order to permute bit sequences.

Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points.

Similarly, a circular shift of the input corresponds to multiplying the output by a linear phase.

Curiously, permutations created in this way (and their circular shifts) have been shown to be Costas arrays.

Others provide only logical or only circular shifts, and arithmetic shifts must be constructed from these basic operations.

In practice, it is more likely that will be a simple linear shift of , rather than a circular shift as required by the explanation above.

A bitonic sequence is a sequence with for some , or a circular shift of such a sequence.

The scalar triple product is invariant under a circular shift of its three operands (a, b, c):

A circular shift is a special kind of cycle, which in turn is a special kind of permutation.

In computer programming, a circular shift (or bitwise rotation) is a shift operator that shifts all bits of its operand.

For example, the DEC PDP-8 computer provides only one- and two-bit circular shifts.

Unlike an arithmetic shift, a circular shift does not preserve a number's sign bit or distinguish a number's exponent from its mantissa.

These may be grouped into sets of p words that can be transformed into each other by circular shifts; these sets are called necklaces.

Cyclic codes are a kind of block code with the property that the circular shift of a codeword will always yield another codeword.

Rotation (which in the FFT is multiplication by a complex phasor) is a circular shift of the component waveform.

We define a pair of words in A of the form uv and vu as conjugate: the conjugates of a word are thus its circular shifts.

(a, b, c, d) (the original four-tuple), and then the sequence repeats; this four-tuple therefore has four distinct circular shifts.

In general the number of circular shifts of an n-tuple could be any divisor of n, depending on the entries of the tuple.

A ring counter is a circular shift register which is initiated such that only one of its flip-flops is the state one while others are in their zero states.