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A processor has 64 registers and uses 16-bit instruction format. It has two types of instructions: I-type and R-type. Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value. Each R-type instruction contains an opcode and two register names. If there are 8 distinct I-type opcodes, then the maximum number of distinct R-type opcodes is ________.
Correct answer is '14'. Can you explain this answer?
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Verified Answer
A processor has 64 registers and uses 16-bit instruction format. It ha...
Given, 16 bit instruction and 64 registers
I-type:
R-type:
1. Primitive instruction
R-type:
2. Number of operation possible = 24 = 16
3. Number of tree opcodes = (16 – x)
Assume x is number of R-type instruction existed.
4. Number of I-type instruction possible = (16 – x) × 22
8 = 64 – 4 x
4x = 64 – 8 = 56
x = 56/4 ⇒ 14
I-type:
R-type:
1. Primitive instruction
R-type:
2. Number of operation possible = 24 = 16
3. Number of tree opcodes = (16 – x)
Assume x is number of R-type instruction existed.
4. Number of I-type instruction possible = (16 – x) × 22
8 = 64 – 4 x
4x = 64 – 8 = 56
x = 56/4 ⇒ 14
Most Upvoted Answer
A processor has 64 registers and uses 16-bit instruction format. It ha...
To find the maximum number of distinct R-type opcodes, we need to consider the number of bits available for the opcode in the 16-bit instruction format and the constraints given in the problem.
Given information:
- Processor has 64 registers
- Instruction format is 16-bit
- Two types of instructions: I-type and R-type
- Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value
- Each R-type instruction contains an opcode and two register names
- 8 distinct I-type opcodes
Calculating the number of bits available for the opcode:
In a 16-bit instruction format, the opcode can occupy a certain number of bits. To find this number, we subtract the bits occupied by other components of the instruction (register names and immediate value) from the total number of bits in the instruction format.
- Register name: Since there are 64 registers, we need 6 bits to represent each register (2^6 = 64). Therefore, the total bits occupied by the register name in an instruction is 2 * 6 = 12 bits.
- Immediate value: Given that the immediate value is a 4-bit value, it occupies 4 bits in the instruction.
Total bits occupied by other components: 12 bits (register name) + 4 bits (immediate value) = 16 bits.
Therefore, the number of bits available for the opcode is 16 - 16 = 0.
Determining the maximum number of distinct R-type opcodes:
Since there are 0 bits available for the opcode in the 16-bit instruction format, we cannot have any distinct R-type opcodes. All R-type instructions would have the same opcode, making it impossible to differentiate between different R-type instructions based on their opcodes.
Hence, the maximum number of distinct R-type opcodes is 0, not 14 as stated in the question.
Given information:
- Processor has 64 registers
- Instruction format is 16-bit
- Two types of instructions: I-type and R-type
- Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value
- Each R-type instruction contains an opcode and two register names
- 8 distinct I-type opcodes
Calculating the number of bits available for the opcode:
In a 16-bit instruction format, the opcode can occupy a certain number of bits. To find this number, we subtract the bits occupied by other components of the instruction (register names and immediate value) from the total number of bits in the instruction format.
- Register name: Since there are 64 registers, we need 6 bits to represent each register (2^6 = 64). Therefore, the total bits occupied by the register name in an instruction is 2 * 6 = 12 bits.
- Immediate value: Given that the immediate value is a 4-bit value, it occupies 4 bits in the instruction.
Total bits occupied by other components: 12 bits (register name) + 4 bits (immediate value) = 16 bits.
Therefore, the number of bits available for the opcode is 16 - 16 = 0.
Determining the maximum number of distinct R-type opcodes:
Since there are 0 bits available for the opcode in the 16-bit instruction format, we cannot have any distinct R-type opcodes. All R-type instructions would have the same opcode, making it impossible to differentiate between different R-type instructions based on their opcodes.
Hence, the maximum number of distinct R-type opcodes is 0, not 14 as stated in the question.
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A processor has 64 registers and uses 16-bit instruction format. It has two types of instructions: I-type and R-type. Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value. Each R-type instruction contains an opcode and two register names. If there are 8 distinct I-type opcodes, then the maximum number of distinct R-type opcodes is ________.Correct answer is '14'. Can you explain this answer?
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