Provide the minimal set of LEGv8 instructions that may be used to implement the following pseudo- instruction

Provide the minimal set of LEGv8 instructions that may be used to implement the following pseudo- instruction: G0%) NOT X12, X13 ll bit-wise invert operation

The Correct Answer and Explanation is :

The pseudo instruction NOT X12, X13 performs a bitwise NOT operation, which inverts the bits of the value stored in X13 and stores the result in X12. In LEGv8, the NOT instruction doesn’t exist as a native operation, so we must implement it using the minimal set of available instructions.

Minimal set of LEGv8 instructions:

EOR X12, X13, X13, LSL #0
ADD X12, X12, XZR

Explanation:

1. EOR (Exclusive OR) Instruction:

   EOR X12, X13, X13, LSL #0

The EOR instruction performs an exclusive OR (XOR) operation between two registers. The result of the XOR operation is 1 when the corresponding bits of the two operands are different, and 0 when they are the same.

By performing EOR X13, X13, X13, LSL #0, we effectively XOR register X13 with itself. The result of this XOR operation will be a register with all bits set to 0. However, the key insight here is that this operation also allows us to control the inversion behavior by using the Logical Shift Left (LSL #0), which ensures that X13 is unchanged by the shift but can still be utilized for the operation.

2. ADD Instruction:

   ADD X12, X12, XZR

After the EOR operation, the content in X12 is now the complement of the original value in X13. However, the ADD X12, X12, XZR instruction is needed to store the result effectively. XZR is the zero register, which is always 0, so this ADD instruction has the effect of copying the value from X12 into itself, ensuring that the result is correctly placed.

This instruction is necessary because, without it, the original value of X12 might be undefined.

Why this works:

• The XOR operation inverts each bit of X13, which is equivalent to the NOT operation.
• The ADD instruction is simply used to finalize the result by copying the inverted value from X12 into the destination register.

These two instructions achieve the desired result with minimal instruction usage.