JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III COMPUTER ORGANIZATION AND OPERATING SYSTEMS Previous Question Paper (September - 2021 - R13)

Floating-point representation is used to represent real numbers that are either very large or very small, which cannot be accommodated in a standard fixed-point format. It follows the IEEE 754 standard, which represents a number as: N = (-1)^S × M × 2^E. Here, S represents the sign bit, M is the mantissa (or significand), and E is the exponent.

The representation is typically divided into three fields:

• Sign bit (S): A single bit that indicates the sign of the number. 0 represents a positive number, and 1 represents a negative number.
• Exponent (E): This field stores the exponent value, usually in a biased format to allow for both positive and negative exponents without needing a separate sign bit for the exponent field itself.
• Mantissa (M): Also called the significand, this represents the precision bits of the number. In normalized form, it is represented as 1.f, where the leading 1 is implicit in many formats to save space.

For single-precision (32-bit) format, the structure is:

For double-precision (64-bit) format, the structure is:

To normalize a number, the mantissa is shifted until the leading digit is non-zero (in binary, this is always 1). The exponent is then adjusted accordingly. This ensures a unique representation for every number and maximizes the precision of the stored value.

An addressing mode specifies the manner in which the effective address of an operand is calculated or how the operand itself is represented within an instruction. It defines the relationship between the address field of an instruction and the actual location of the data in memory or registers.

The following are the primary types of addressing modes:

• Implied Addressing: The operand is implicitly defined in the definition of the instruction itself (e.g., CLC - Clear Carry). No address field is required.
• Immediate Addressing: The operand is provided directly within the instruction. It is useful for initializing registers with constant values.
• Register Addressing: The operand is stored in a CPU register. The instruction contains the register name, which is faster than memory access.
• Register Indirect Addressing: The instruction specifies a register that contains the memory address of the operand. This allows for dynamic memory access.
• Direct Addressing: The instruction contains the actual effective address of the operand in memory.
• Indirect Addressing: The instruction contains a memory address that points to another memory location where the actual operand address is stored.
• Indexed Addressing: The effective address is calculated by adding a constant value (displacement) to the contents of an index register. This is essential for accessing arrays.
• Base Register Addressing: The effective address is the sum of a base register and an offset. This is commonly used for program relocation and accessing data structures.
• Relative Addressing: The effective address is calculated by adding a displacement value to the current Program Counter (PC). This facilitates position-independent code.