Bitwise Operations

Bitwise Operations are operations that are performed bit-by-bit on one or two operands (input values) to produce an output value.

Logical Bitwise Operations

Logical bitwise operations are performed by executing a logical operation such as OR, AND, or XOR on operands, processing corresponding bits in each operand. For example, the logical OR operation takes a two-bit input and produces a one-bit output. When applied bitwise to two 32-bit values, a logical OR is performed using bit 0 (the least significant bit) of each of the two operands as input, and the result is stored in bit 0 of the output. Bit 1 of the two operands is processed to produce bit 1 of the output, and so forth.

For most logical bitwise operations, one operand is viewed as the input, and the other operand is viewed as a mask.

True and False
True is represented by binary 1, and false is represented by binary 0, in the textual descriptions of logical operations below.

OR

The OR logical operation takes two inputs, labelled A and B, and produces an output.

Written out as a text description, OR means:

If A OR B are true, then the OUTPUT is true.

The truth table looks like this:

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

This can be reduced to:

Input	Mask	Output
X	0	X
X	1	1

When applied bitwise:

Wherever a 0 appears in the Mask, the corresponding bit in the Input appears unchanged in the Output
Wherever a 1 appears in the Mask, the corresponding bit is a 1 in the Output

Therefore the bitwise OR is used to set bits to a value of 1.

For example, bits 4:7 can be set to 1 while preserving the remaining bits in a byte by ORing a mask of 11110000 (0xF0):

	Bit 7	Bit 6	Bit 5	Bit 4	Bit 3	Bit 2	Bit 1	Bit 0
Input	0	1	0	1	0	1	0	1
Mask	1	1	1	1	0	0	0	0
Output	1	1	1	1	0	1	0	1

AND

The OR logical operation means:

If A AND B are true, then the OUTPUT is true.

The truth table looks like this:

A	B	Output
0	0	0
0	1	0
1	0	0
1	1	1

This can be reduced to:

Input	Mask	Output
X	0	0
X	1	X

When applied bitwise:

Wherever a 0 appears in the Mask, the corresponding bit is a 0 in the Output
Wherever a 1 appears in the Mask, the corresponding bit in the Input appears unchanged in the Output

Therefore the bitwise AND is used to clears bits to a value of 0.

For example, bits 0:3 can be cleared to 0 while preserving the remaining bits in a byte by ANDing a mask of 11110000 (0xF0):

	Bit 7	Bit 6	Bit 5	Bit 4	Bit 3	Bit 2	Bit 1	Bit 0
Input	0	1	0	1	0	1	0	1
Mask	1	1	1	1	0	0	0	0
Output	0	1	0	1	0	0	0	0

XOR

The XOR (Exclusive OR) logical operation means:

If A AND B are true, but not both, then the OUTPUT is true.

The truth table looks like this:

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	0

This can be reduced to:

Input	Mask	Output
X	0	X
X	1	!X

Where !X means "not X" or "X inverted" (0 becomes 1; 1 becomes 0).

When applied bitwise:

Wherever a 0 appears in the Mask, the corresponding bit appears unchanged in the Output
Wherever a 1 appears in the Mask, the corresponding bit in the Input is inverted in the Output

Therefore the bitwise XOR is used to flip (invert) bits from 0 to 1 and vice-versa.

For example, bits 4:7 can be flipped while preserving the remaining bits in a byte by XORing a mask of 11110000 (0xF0):

	Bit 7	Bit 6	Bit 5	Bit 4	Bit 3	Bit 2	Bit 1	Bit 0
Input	0	1	0	1	0	1	0	1
Mask	1	1	1	1	0	0	0	0
Output	1	0	1	0	0	1	0	1

NOT

NOT is a unary operation which inverts all bits.

The Output is the inverse of the Input.

The truth table looks like this:

A	Output
0	1
1	0

Bitwise:

	Bit 7	Bit 6	Bit 5	Bit 4	Bit 3	Bit 2	Bit 1	Bit 0
Input	0	1	0	1	0	1	0	1
Output	1	0	1	0	1	0	1	0

NAND

NAND is an AND operation with the output inverted.

NOR

NOR is an OR operation with the output inverted.

Bit shifts and rotates

Bit shift and rotate operations are used to move bits to the left or right within a word.

Rotate

A rotate operation moves bits right or left. Bits shifted out of the word are moved to the other end.

A rotate-right by 1 bit performed on a byte will move bit 7 to bit 6, bit 6 to bit 5, bit 5 to bit 4, and so forth. Bit 0 will move to bit 7.

A rotate-left by 1 bit performed on a byte will move bit 0 to bit 1, bit 1 to bit 2, bit 2 to bit 3, and so forth. Bit 7 will move to bit 0.

Note that in some processors, a status register bit is included in the rotation, allowing rotates to be strung together in multi-byte sequences.

Shift

Shift operations are like rotate operations, but bits shifted out of the word are either lost or placed in a processor flag, and bits shifted in are either 0 or from a processor flag.

Note that a binary left-shift is equivalent to multiply-by-2, and right-shift is equivalent to divide-by-2.