Question: A MIPS “I-Format” Immediate Value As An Unsigned Constant Can Range From 0 To:
The Correct Answer and Explanation is:
Correct Answer:
65,535
Explanation:
In MIPS (Microprocessor without Interlocked Pipeline Stages) architecture, the I-format (Immediate format) is one of the instruction formats used for operations involving constants (immediate values) and addresses. Examples include instructions such as addi, andi, ori, lw, sw, and beq.
Structure of I-Format:
An I-format instruction in MIPS is 32 bits long and structured as follows:
- 6 bits: Opcode (specifies the operation, e.g.,
addi,lw,beq) - 5 bits: Source register (rs)
- 5 bits: Destination register (rt)
- 16 bits: Immediate value (constant or offset)
Understanding the 16-bit Immediate Field:
The immediate field in I-format is 16 bits long. The way this field is interpreted depends on the type of instruction and whether the value is treated as signed or unsigned.
- For instructions like
addi(add immediate), the 16-bit immediate is sign-extended to 32 bits, meaning it is treated as a signed integer in the range: - −32,768 to +32,767
- For instructions like
andi,ori, andxori, the immediate is treated as zero-extended — in other words, as an unsigned integer.
Unsigned Immediate Range:
Since the immediate field is 16 bits and is treated as unsigned in logical instructions (like andi and ori):
- The minimum unsigned value is 0
- The maximum unsigned value is 2¹⁶ − 1 = 65,535
This is because:
$$
\text{Range of unsigned 16-bit value} = 0 \text{ to } (2^{16} – 1) = 0 \text{ to } 65535
$$
Thus, in MIPS I-format instructions where the immediate is treated as an unsigned constant, the range is 0 to 65,535.
Conclusion:
When the 16-bit immediate in a MIPS I-format instruction is interpreted as an unsigned constant, its range is from 0 to 65,535.
