Difference between revisions of "Bitwise Operations"
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= | == Curriculum == | ||
{{MerlinCurriculumData|{{ROOTPAGENAME}}}} | |||
== | == Bitwise Operations == | ||
A bitwise operation operates on one or more bit patterns at the level of their individual bits. It is a fast, simple action supported by the ALU (Arithmetic Logic Unit) and is used to manipulate values for comparisons and calculations. The normal operation is simply applied bit by bit. | A bitwise operation operates on one or more bit patterns at the level of their individual bits. It is a fast, simple action supported by the ALU (Arithmetic Logic Unit) and is used to manipulate values for comparisons and calculations. The normal operation is simply applied bit by bit. | ||
=== NOT === | |||
<pre> | <pre> | ||
NOT 0111 | NOT 0111 | ||
| Line 9: | Line 9: | ||
= 1000 | = 1000 | ||
</pre> | </pre> | ||
{{Caution|Note that because zero bits are "flipped" to one bits the actual size of the word matters. For example, | |||
<pre> | |||
NOT 0111 | |||
= 1000 | |||
</pre> | |||
when considering only a four-bit word, but in the case of an eight-bit word the correct answer would be: | |||
<pre> | |||
= 1111 1000 | |||
</pre> | |||
As such, it's usually best to left-pad the operand with zeroes before proceeding. For example, | |||
<pre> | |||
NOT 0000 0111 | |||
= 1111 1000 | |||
</pre> | |||
}} | |||
=== AND === | |||
The AND operation is useful for masking bits that are not interesting and then checking to see if a particular bit is set. | The AND operation is useful for masking bits that are not interesting and then checking to see if a particular bit is set. | ||
<pre> | <pre> | ||
0101 | 0101 | ||
| Line 18: | Line 32: | ||
= 0001 | = 0001 | ||
</pre> | </pre> | ||
=== OR === | |||
<pre> | <pre> | ||
0101 | 0101 | ||
| Line 25: | Line 39: | ||
= 0111 | = 0111 | ||
</pre> | </pre> | ||
=== XOR === | |||
The XOR operation is useful for inverting selected bits: | The XOR operation is useful for inverting selected bits: | ||
<pre> | <pre> | ||
0101 | 0101 | ||
| Line 43: | Line 56: | ||
= 0000 | = 0000 | ||
</pre> | </pre> | ||
== Exercises == | |||
{{W1015-Exercises}} | |||
{{Experience | |||
|experienceID=W1015 | |||
|experienceUnit=Boolean algebra | |||
|knowledgeAndSkills=§10.326 | |||
|topicAreas=Boolean algebra | |||
|classroomTime=10 minutes | |||
|studyTime=1 hour | |||
|acquiredKnowledge=understand the use of bitwise operations with common Boolean operators | |||
|acquiredSkill=demonstrate proficiency in using bitwise operations with common Boolean operators | |||
}} | |||
Revision as of 03:04, 22 June 2021
Curriculum[edit]
 |
Coder Merlin™ Computer Science Curriculum Data |
|
Unit: Boolean algebra Experience Name: Bitwise Operations (W1015) Next Experience: () Knowledge and skills:
Topic areas: Boolean algebra Classroom time (average): 10 minutes Study time (average): 60 minutes Successful completion requires knowledge: understand the use of bitwise operations with common Boolean operators Successful completion requires skills: demonstrate proficiency in using bitwise operations with common Boolean operators |
Bitwise Operations[edit]
A bitwise operation operates on one or more bit patterns at the level of their individual bits. It is a fast, simple action supported by the ALU (Arithmetic Logic Unit) and is used to manipulate values for comparisons and calculations. The normal operation is simply applied bit by bit.
NOT[edit]
NOT 0111 ———————— = 1000
NOT 0111 = 1000
when considering only a four-bit word, but in the case of an eight-bit word the correct answer would be:
= 1111 1000
As such, it's usually best to left-pad the operand with zeroes before proceeding. For example,
NOT 0000 0111 = 1111 1000
AND[edit]
The AND operation is useful for masking bits that are not interesting and then checking to see if a particular bit is set.
0101 AND 0011 ———————— = 0001
OR[edit]
0101 OR 0011 ———————— = 0111
XOR[edit]
The XOR operation is useful for inverting selected bits:
0101 XOR 0011 ———————— = 0110
Because of this property, XOR is sometimes used to clear a register (to zero) by XOR’ing it with itself. In some cases this can be much faster than explicitly loading the value of 0.
1010 XOR 1010 ———————— = 0000
Exercises[edit]
Experience Metadata
| Experience ID | W1015 |
|---|---|
| Next experience ID | |
| Unit | Boolean algebra |
| Knowledge and skills | §10.326 |
| Topic areas | Boolean algebra |
| Classroom time | 10 minutes |
| Study time | 1 hour60 minutes <br /> |
| Acquired knowledge | understand the use of bitwise operations with common Boolean operators |
| Acquired skill | demonstrate proficiency in using bitwise operations with common Boolean operators |
| Additional categories |
