Insight on Arithmetic Micro Operations

A register is a group of flip-flops. Each of these flip-flops are capable of storing one bit of information. An n-bit register has a group of n flip-flops and is capable of storing binary information of n-bits.

A register consists of a group of flip-flops and gates. The flip-flops hold the binary information and the gates control when and how new information is transferred into a register. Various types of registers are available commercially. The simplest register is one that consists of only flip-flops with no external gates.

These days registers are also implemented as a register file.

What are Micro Operations?

Any operation executed on data that are stored in registers is called a micro operation. A micro operation can also be defined as an elementary operation that is performed on the information stored in one or more registers. 

Example:  Shift, count, load etc.

Types of Micro-Operations

There are 4 types of micro-operations in digital computers:

1. Register transfer micro-operations transfer binary information from one register to another.
2. Arithmetic micro-operations perform arithmetic operations on numeric data stored in registers.
3. Logic micro-operations perform bit manipulation operation on non-numeric data stored in registers.
4. Shift micro-operations perform shift micro-operations performed on data.

Arithmetic Micro Operations

Let us look at Arithmetic micro operations in detail.

Add Micro Operation

This is defined by the following expression:

R3 → R1 + R2

The above statement gives an instruction to the data or the contents that are stored in R1 to be added to the data or content of R2. The sum of these data or contents are transfered to register R3.

Subtract Micro Operation

R3 → R1 + R2' + 1

 The above statement denotes the subtract micro operation. Here, instead of using the minus operator we use 1's compliment and add 1 to the register which gets subtracted. 

i.e R1-R2  is equivalent to R3 → R1 + R2' + 1

Increment/Decrement Micro Operation

This micro operation is generally performed by adding and subtracting 1 to and from the register respectively.

 R1 → R1 + 1

 R1 → R1 - 1

The following table is a representation and description of the various symbolic designations:

Symbolic Designation	Description
R3 ← R1 + R2	Contents of R1+R2 transferred to R3.
R3 ← R1 - R2	Contents of R1-R2 transferred to R3.
R2 ← (R2)'	Compliment the contents of R2.
R2 ← (R2)' + 1	2's compliment the contents of R2.
R3 ← R1 + (R2)' + 1	R1 + the 2's compliment of R2 (subtraction).
R1 ← R1 + 1	Increment the contents of R1 by 1.
R1 ← R1 - 1	Decrement the contents of R1 by 1.

Logic Micro Operation

Logic micro operations can be defined as binary micro operations that are performed on each of the bits stored on a register. These bits take each bit into consideration separately and treat them as binary values.

Let us consider an example of X-OR micro operation with the contents of two registers R1 and R2.

P: R1 ← R1 X-OR R2

A control function has also been included in the above statement.

Assuming that each of the registers have 3 bits, let R1 has 010 and R2 has 100. The X-OR micro operation will be: 

Shift Micro Operation

These are used for serial transfer of data. That means we can shift the contents of the register to the left or right. In the shift left operation the serial input transfers a bit to the right most position and in shift right operation the serial input transfers a bit to the left most position.

There are three types of shifts as follows:

a) Logical Shift

It transfers 0 through the serial input. The symbol "shl" is used for logical shift left and "shr" is used for logical shift right.

R1 ← shl R1 

R1 ← shr R1 

b) Circular Shift

This circulates or rotates the bits of register around the two ends without any loss of data or contents. In this, the serial output of the shift register is connected to its serial input. "cil" and "cir" is used for circular shift left and right respectively.

c) Arithmetic Shift

This shifts a signed binary number to left or right. An arithmetic shift left multiplies a signed binary number by 2 and shift left divides the number by 2. Arithmetic shift micro-operation leaves the sign bit unchanged because the signed number remains same when it is multiplied or divided by 2.

The above diagram is a simple representation of  some Arithmetic  micro operations

The given video below explains on detail the various types of arithmetic micro operations and a pictorial representation  for easier understanding of micro operations, their functions and how they work.

 

References:

https://www.studytonight.com/computer-architecture/registers

https://www.youtube.com/arithmetic-micro-operations

https://www.scribd.com/presentation/152759649/Arithmetic-Micro-operations-and-Logic-Micro-operations