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A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0).
In a binary search tree, a right rotation is the movement of a node, X, down to the right. This rotation assumes that X has a left child (or subtree). X's left child, R, becomes X's parent node and R's right child becomes X's new left child. This rotation is done to balance the tree; specifically when the left subtree of node X has a ...
The two basic types are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in.
It can also be described as the shortest path distance in a rotation graph, a graph that has a vertex for each binary tree on a given left-to-right sequence of nodes and an edge for each rotation between two trees. [2] This rotation graph is exactly the graph of vertices and edges of an associahedron. [3]
A tree can be rebalanced using rotations. After a rotation, the side of the rotation increases its height by 1 whilst the side opposite the rotation decreases its height similarly. Therefore, one can strategically apply rotations to nodes whose left child and right child differ in height by more than 1.
It is performed by reading the binary number from left to right, doubling if the next bit is zero, and doubling and adding one if the next bit is one. [5] In the example above, 11110011, the thought process would be: "one, three, seven, fifteen, thirty, sixty, one hundred twenty-one, two hundred forty-three", the same result as that obtained above.
The bitwise XOR (exclusive or) performs an exclusive disjunction, which is equivalent to adding two bits and discarding the carry. The result is zero only when we have two zeroes or two ones. [3] XOR can be used to toggle the bits between 1 and 0. Thus i = i ^ 1 when used in a loop toggles its values between 1 and 0. [4]
Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n. Shifting right by n bits on an unsigned binary number has the effect of dividing it by 2 n (rounding towards 0). Logical right shift differs from arithmetic right shift. Thus, many languages have different operators for them.