Define the arithmetic micro-operations, Computer Engineering

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Q. Define the Arithmetic Micro-operations?

These micro-operations execute simple arithmetic operations on numeric data stored in registers. The fundamental arithmetic micro-operations are subtraction, addition, decrement, increment and shift. 

Addition micro-operation is expressed as:

      R3 ← R1 +R2 

It means that contents of register R1 are added to contents of register R2 and sum is transferred to register R3. This operation needs three registers to hold data along with Binary Adder circuit in the ALU. Binary adder is a digital circuitthat produces the arithmetic sum of two binary numbers of any lengths and is constructed with full-adder circuits associated in cascade. An n-bit binary adder needs n full-adders. Add micro-operation in accumulator machine can be performed as:

AC ← AC + DR

Subtraction is most frequently implemented in machines through complement and adds operations. It is specified as:

        R3 ← R1 - R2  

        R3 ← R1 + (2's complement of R2)

        R3 ← R1 + (1's complement of R2 + 1)

        R3 ← R1 + R2 + 1 (The bar on top of R2 implies 1's complement of R2 that is bitwise complement)    

Adding 1 to 1's complement generates the 2's complement. Adding contents of R1 to the 2's complement of R2 is equal to subtracting contents of R2 from R1 and storing the result in R3.

The increment micro-operation adds one to a number in a register. This operation is expressed as:

                 R1 ← R1 + 1

This can be implemented in hardware by employing a binary-up counter.  

The decrement micro-operation subtracts one from a number in a register. This operation is expressed as:

                 R1 ← R1 - 1 

This can be implemented by binary-down counter.

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