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[[Category:Computer Architecture]]
''Bitwise Operations'' are [[Operation|operations]] that are performed on [[Word#Bit|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''.
{{Admon/note|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 means:
If A ''OR'' B are true, then the OUTPUT is true.
The truth table looks like this:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||1
|-align="center"
|1||0||1
|-align="center"
|1||1||1
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||X
|-align="center"
|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):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||0||1||0||1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Mask ||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||0||0||0||0
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0
|}
=== AND ===
The ''OR'' logical operation means:
If A ''AND'' B are true, then the OUTPUT is true.
The truth table looks like this:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||0
|-align="center"
|1||0||0
|-align="center"
|1||1||1
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||0
|-align="center"
|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):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||0||1||0||1
|-align="center"
|Mask ||1||1||1||1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0
|-align="center"
|Output||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|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:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||1
|-align="center"
|1||0||1
|-align="center"
|1||1||0
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||X
|-align="center"
|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 0-3 can be flipped while preserving the remaining bits in a byte by XORing a mask of 11110000 (0xF0):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Mask ||bgcolor="orange"|1||bgcolor="orange"|1||bgcolor="orange"|1||bgcolor="orange"|1||0||0||0||0
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|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:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|Output
|-align="center"
|0||1
|-align="center"
|1||0
|}
Bitwise:
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input ||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|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|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.
=== Shift ===
Shift operations are like rotate operations, but bits shifted out of the word are either lost or placed in a processor [[Register#Status Register|flag]], and bits shifted in are either 0 or from a processor flag.
''Bitwise Operations'' are [[Operation|operations]] that are performed on [[Word#Bit|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''.
{{Admon/note|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 means:
If A ''OR'' B are true, then the OUTPUT is true.
The truth table looks like this:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||1
|-align="center"
|1||0||1
|-align="center"
|1||1||1
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||X
|-align="center"
|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):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||0||1||0||1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Mask ||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||0||0||0||0
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0
|}
=== AND ===
The ''OR'' logical operation means:
If A ''AND'' B are true, then the OUTPUT is true.
The truth table looks like this:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||0
|-align="center"
|1||0||0
|-align="center"
|1||1||1
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||0
|-align="center"
|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):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||0||1||0||1
|-align="center"
|Mask ||1||1||1||1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0
|-align="center"
|Output||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|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:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|B!!width="34%"|Output
|-align="center"
|0||0||0
|-align="center"
|0||1||1
|-align="center"
|1||0||1
|-align="center"
|1||1||0
|}
This can be reduced to:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|Input!!width="33%"|Mask!!width="34%"|Output
|-align="center"
|X||0||X
|-align="center"
|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 0-3 can be flipped while preserving the remaining bits in a byte by XORing a mask of 11110000 (0xF0):
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Mask ||bgcolor="orange"|1||bgcolor="orange"|1||bgcolor="orange"|1||bgcolor="orange"|1||0||0||0||0
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|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:
{|cellspacing="0" cellpadding="5" border="1"
!width="33%"|A!!width="33%"|Output
|-align="center"
|0||1
|-align="center"
|1||0
|}
Bitwise:
{|cellspacing="0" cellpadding="5" border="1"
! !!Bit 7!!Bit 6!!Bit 5!!Bit 4!!Bit 3!!Bit 2!!Bit 1!!Bit 0
|-align="center"
|Input ||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1
|-align="center"
|Output||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|0||bgcolor="yellow"|1||bgcolor="yellow"|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|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.
=== Shift ===
Shift operations are like rotate operations, but bits shifted out of the word are either lost or placed in a processor [[Register#Status Register|flag]], and bits shifted in are either 0 or from a processor flag.
