Logic Micro Operations in Computer Architecture - Coding Ninjas CodeStudio

Q: What are the applications of logic microoperations?

Logical microoperations are used in digital circuits, arithmetic logic units, MUX (multipliers), DEMUX (demultiplexers), data encryption, hashing, memory addressing, decoding, bit masking, communication systems, digital system design, and digital signal processing.

Q: What is the hardware implementation of logic micro-operation?

In hardware implementation of logic micro-operations, we need to insert gates like AND, NOT, OR, and EXOR for each individual bit or pair of bits. The basic logic gates are combined to implement complex micro-operations.

Q: What is the importance of logic operation?

Logical microoperations play an essential role in digital electronics. They are used to frame a way in which the information flows through the circuits. Logical microoperations consume less power. Therefore it helps in building low-power consumption systems. They are easy to scale and can hold larger amounts of datasets.

Introduction

As you know, a computer works on instructions. Our systems consist of machine instructions to perform some operations like add, subtract, multiply, divide etc. To perform these operations, the system stores the data in registers. Now, to operate this data, the CPU has micro-operations. A micro-operation is a simple operation performed on the data stored in one or more registers. They transfer the data between registers. There are four types of micro-operations:-

Register micro-operations
Arithmetic micro-operations
Logic micro-operations
Shift micro-operations

In this blog, we will discuss logic micro-operations.

What are Logic Micro-Operations?

Logic Microoperations are a set of binary operations that are performed on registers that contain strings of bits. These operations treat each bit of the register separately and consider them as binary variables. As a result, there are 16 different logic operations that could be performed. These are-

Before discussing these logic micro-operations, let’s discuss their truth tables.

The below diagram shows the truth table for all the 16 logic micro-operations mentioned above. Here, x and y are the variables or registers in which the data is stored and F0, F1, ….., F15 are the outputs that occur after performing these logic micro-operations.

Now, we will discuss these logic micro-operations one by one.

1. Clear

The Clear logic micro-operation is used to clear the register or set the bits of the register to 0. To use this micro-operation, we need to feed 0 to the register. In the above truth table, F0 represents the truth table of Clear logic micro-operation.

For example, F <- 0 means the value of the register F is set to 0 or is cleared. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Clear logic micro-operation is F0 = 0

2. AND

The AND logic micro-operation performs the logical AND between the bits of the data stored in the two registers. The symbol to represent the logical AND is ∧ .

Case 1: Both x and y values are true.

In the first case, if the values of both two registers are true then the result of AND operation is 1; else, it is 0. F1 represents the truth table of AND logic micro-operation in the above truth table.

For example, F <- A ∧ B means the registers A and B value will undergo AND micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the AND logic micro-operation will be F1 = x.y

Case 2: x is true, and y is false.

The logical AND operation we discussed above gives output 1 when both x and y are true. There is also another AND operation which includes x but not y. Also known as inhibition, here for performing the AND operation, the first value is taken from the x variable or register. The second value is taken as the complement of the y variable or register. If the value of the x register is true and of the y register is false, then the result of AND operation is 1; else, it is 0.

F2 represents the truth table of inhibition AND logic micro-operation in the above truth table.

For example, F <- A ∧ B’ means the value of the registers A and complement B will undergo AND micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the AND logic micro-operation will be F2 = x.y’

Case 3: x is false, and y is true.

The third case of logical AND operation includes y but not x. Also known as inhibition, here for performing the AND operation, the first value is taken as the complement of the x variable or register, and the second value is taken from the y variable or register. If the value of the x register is false and of the y register is true, then the result of AND operation is 1; else, it is 0.

F4 represents the truth table of inhibition AND logic micro-operation in the above truth table.

For example, F <- A’ ∧ B means the value of the complement register A and as it is B will undergo AND micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the AND logic micro-operation will be F4 = x’.y

3. Transfer A

The Transfer A logic micro-operation transfers the contents of register A (first register) to the output register.

F3 represents the truth table of Transfer A logic micro-operation in the above truth table. Since there is a transfer of data from the first register to the output register in this micro-operation, its truth table is the same as the taken values of the x variable (0, 0, 1, 1).

For example, F <- A means the value of register A is moved to register F. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Transfer A logic micro-operation is F3 = x

4. Transfer B

The Transfer B logic micro-operation transfers the contents of register B (second register) to the output register.

F5 represents the truth table of Transfer B logic micro-operation in the above truth table. Since there is a transfer of data from the second register to the output register in this micro-operation, its truth table is the same as the taken values of the y variable (0, 1, 0, 1).

For example, F <- B means the value of register B is moved to register F. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Transfer B logic micro-operation is F5 = y

5. Exclusive OR

Also known as XOR, this logic micro-operation performs the logical XOR between the data bits stored in the two registers. The logical XOR means either x should be true or y but not both. The symbol to represent the Exclusive OR is ⊕.

F6 represents the truth table of Exclusive OR logic micro-operation in the above truth table. The output will be 1 when either x =1 and y = 0 or x = 0 and y = 1.

For example, F <- A ⊕ B means the registers A and B value will undergo XOR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the Exclusive OR logic micro-operation will be F6 = x.y’ + x’.y

6. OR

The OR logic micro-operation performs the logical OR between the data bits stored in the two registers. The symbol to represent the logical OR is ∨.

Case 1: Either x or y or both x and y values are true.

In the first case, if either the value of x register is true and y register is false, or the value of x register is false, and y register is true, or both the values of x and y registers are true, then the result of OR operation is 1 else it is 0. F7 represents the truth table of OR logic micro-operation in the above truth table.

For example, F <- A ∨ B means the registers A and B value will undergo OR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the OR logic micro-operation will be F7 = x + y

Case 2: If y, then x else not.

In the second case, the output for 1 follows the condition that

If the value of the y register is true, then the value of the x register must be true. If this condition is satisfied, then the output is 1.
If the value of the y register is false, then we don’t need to look for the value of the x register, and the output is 1.
Else the output is 0.

To perform this logic micro-operation, we need to perform the logical OR of the values of the x register and the complement value of the y register.

In the above truth table, F11 represents the truth table of this logic micro-operation.

For example, F <- A ∨ B’ means the value of the registers A and complement B will undergo OR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for this OR logic micro-operation will be F11 = x + y’

Case 3: If x, then y else not.

In the second case, the output for 1 follows the condition that

If the value of the x register is true, then the y register's value must be true. If this condition is satisfied, then the output is 1.
If the value of the x register is 0, then we don’t need to look for the value of the y register, and the output is 1.
Else the output is 0.

To perform this logic micro-operation, we need to perform the logical OR of the complemented value of the x register and the value of the y register.

In the above truth table, F13 represents the truth table of this logic micro-operation.

For example, F <- A’ ∨ B means the complemented register A and B value will undergo OR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for this OR logic micro-operation will be F13 = x’ + y

7. NOR

The NOR logic micro-operation is simply the opposite of OR logic micro-operation. As the name suggests, it is Not OR. The output of OR micro-operation is 1 when the value of either x register or y register or both x and y registers are true. In contrast, in NOR, the output is 0 when the value of either x register or y register or both x and y registers are true, and it is 1 when both x and y registers are false. In the above truth table, F8 represents the truth table of NOR logic micro-operation.

For example, F <- (A ∨ B)’ means the registers A and B value will undergo NOR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the Transfer A logic micro-operation is F8 = (x + y)’

Also see, MVVM Architecture Android

8. Exclusive NOR

If we perform the Exclusive NOR micro-operation, the output will be 1 when the values of both the x and y registers will be the same. They can be true or false, but they have to be the same.

F9 represents the truth table of Exclusive NOR logic micro-operation in the above truth table. The output will be 1 when either x = 0 and y = 0 or x = 1 and y = 1.

For example, F <- (A ⊕ B)’ means the registers A and B value will undergo Exclusive NOR micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the Exclusive NOR logic micro-operation will be F9 = x.y + x’.y’

9. Complement B

The Complement B logic micro-operation transfers the complemented contents of register B (second register) to the output register. First, the content of the register is complemented and then moved to the desired register.

In the above truth table, F10 represents the truth table of Complement B logic micro-operation. Since there is a transfer of complemented data from the second register to the output register in this micro-operation, its truth table is just the opposite of the taken values of the y variable (1, 0, 1, 0).

For example, F <- B’ means the complemented value of register B is moved to register F. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Complement B logic micro-operation is F10 = y’

10. Complement A

The Complement A logic micro-operation transfers the complemented contents of register A (first register) to the output register. First, the content of the register is complemented and then moved to the desired register.

F12 represents the truth table of Complement A logic micro-operation in the above truth table. Since there is a transfer of complemented data from the first register to the output register in this micro-operation, its truth table is just the opposite of the taken values of the y variable (1, 1, 0, 0).

For example, F <- A’ means the complemented value of register A is moved to register F. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Complement A logic micro-operation is F12 = x’

11. NAND

The NAND logic micro-operation is simply the opposite of AND logic micro-operation. As the name suggests, it is Not AND. The output of AND micro-operation is 1 when the value of both the x register and y register is true. In contrast, in NAND, the output is 0 when the value of both x register and y register is true, and it is 1 when either x is false, or y is false, or both are false.

In the above truth table, F14 represents the truth table of NAND logic micro-operation.

For example, F <- (A ∧ B)’ means the registers A and B value will undergo NAND micro-operation, and the output will be stored in register F.

Boolean expression-

The boolean expression for the NAND logic micro-operation is F14 = (x.y)’

12. Set to all 1’s

The set to all 1’s logic micro-operations is used to set all the register bits to 1. To use this micro-operation, we just need to feed 1 to the register. In the above truth table, F15 represents the truth table of Set to all 1’s logic micro-operation.

For example, F <- 1 means the value of the register F is set to 1. The previous value of register F will be removed.

Boolean expression-

The boolean expression for the Clear logic micro-operation is F15 = 1

Must Read: What Is a Motherboard and what is middleware

Examples of Logic Micro Operations in Real-World Computing

Logical microoperations are performed on binary data at a hardware level in the processor. Let's discuss some examples of logical micro-operations in real-world computation.

Logical microoperations are used in MUX (multiplexers) and DEMUX (Demultiplersers). MUX is used in address decoding, data routing, etc. While DEMUX is used in signal demodulation and functions as a serial-to-parallel converter.
Logical microoperations are used in cryptography, image processing, etc., where we need accurate control over the individual bits.
Logical microoperations, such as shift microoperations, are used in data storage, compression algorithms, and in other areas to use memory effectively.
They are used in machine learning algorithms for manipulating the data and for making decisions according to the patterns in the dataset. The algorithms are further used in image recognition, voice recognition, natural language processing, etc.
Logical microoperations are used for masking purposes. The AND microoperation is used to mask bits of a register.
Logical microoperations are used to build arithmetic circuits such as adders and subtracters. They are formed by the combination of XOR, AND, and OR for performing subtraction and addition operations.

Advantages of Logic Micro Operations in Processor Design

Below are some of the advantages of logic micro-operations.

Logical microoperations consume less power. Therefore they help in building low-power consumption systems.
They are easy to scale and can hold larger amounts of datasets.
Logical microoperations can reduce the complexity of computations by breaking them into manageable components so that they can be optimized effectively.
Logic micro-operations are very fast and allow efficient processing of huge amounts of data.
Logical micro-operations are very flexible and can be combined in multiple ways to perform a wide number of computations.

Frequently Asked Questions

Q. What are the applications of logic microoperations?

Logical microoperations are used in digital circuits, arithmetic logic units, MUX (multipliers), DEMUX (demultiplexers), data encryption, hashing, memory addressing, decoding, bit masking, communication systems, digital system design, and digital signal processing.

Q. What is the hardware implementation of logic micro-operation?

In hardware implementation of logic micro-operations, we need to insert gates like AND, NOT, OR, and EXOR for each individual bit or pair of bits. The basic logic gates are combined to implement complex micro-operations.

Q. What is the importance of logic operation?

Logical microoperations play an essential role in digital electronics. They are used to frame a way in which the information flows through the circuits. Logical microoperations consume less power. Therefore it helps in building low-power consumption systems. They are easy to scale and can hold larger amounts of datasets.

Conclusion

To summarise, in this article, we studied logic micro-operation. There are 16 logic micro-operation- Clear, AND, Transfer A, Transfer B, Exclusive OR, OR, NOR, Exclusive NOR, Complement B, Complement A, NAND, and Set to all 1’s. We discussed each micro-operation along with their truth tables and boolean expressions.

If you want to study more about computer organisation and architecture or micro-operations, you can refer to the Library section of Coding Ninjas.

To learn more about Micro Operations, refer to Arithmetic Micro Operations

Check out other blogs on micro-operations, Register in Computer, Repeater in Computer Network, and Bus and Memory Transfer.

Till then, Happy Learning Ninja :)