The Explanation:

The given question is related to addressing modes in computer architecture. An addressing mode is a way to specify the address of an operand in an instruction. Different addressing modes have different ways to calculate the effective address of an operand.

Addressing Modes:

1. Indexed Addressing Mode: In this mode, the content of the index register is added to the address field of the instruction to calculate the effective address. The index register contains a value that is added to the address to access a specific memory location. The effective address is obtained by adding the contents of the index register to the address field.

2. Base Indexed Addressing Mode: In this mode, the contents of both the base register and the index register are added to the address field of the instruction to calculate the effective address. The base register contains a base address, and the index register contains a value that is added to the base address to access a specific memory location. The effective address is obtained by adding the contents of both the base and index registers to the address field.

3. Relative Based Indexed Addressing Mode: In this mode, the contents of the base register, the index register, and a displacement value are added to the address field of the instruction to calculate the effective address. The displacement value is a constant value that is added to the address to access a specific memory location. The effective address is obtained by adding the contents of the base register, index register, and displacement value to the address field.

Answer:

The correct answer is option D, which states that the contents of a base register are added to the contents of an index register in both the based indexed and relative based indexed addressing modes. This means that in both these addressing modes, the effective address is calculated by adding the contents of the base register and the index register. The difference lies in the presence or absence of a displacement value in the relative based indexed addressing mode.

In summary, the base register and index register are used in both the based indexed and relative based indexed addressing modes to calculate the effective address, but the relative based indexed addressing mode also includes a displacement value.