A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is __________.

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Official answer: 16383

Instruction Set and Addressing Modes

Instruction Length: $1\text{ word} = 32\text{ bits}$ .
Opcode Field: The machine supports 45 instructions.
$\text{Opcode bits} = \lceil \log_2 45 \rceil = 6\text{ bits}$
Register Operand Fields: There are 64 registers, so addressing one register requires:
$\lceil \log_2 64 \rceil = 6\text{ bits}$
For 2 register operands, the total bits required are $2 \times 6 = 12\text{ bits}$ .
Immediate Operand Field:
$\text{Remaining bits} = 32 - (\text{Opcode bits} + \text{Register bits}) = 32 - (6 + 12) = 14\text{ bits}$
Maximum Value: For an unsigned 14-bit integer, the maximum value is:
$2^{14} - 1 = 16384 - 1 = 16383$

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This Instruction Set and Addressing Modes previous year question is Q9 of the GATE CSE 2014 Set 1 paper. Find more GATE CSE PYQs on Instruction Set and Addressing Modes in Computer Organization and Architecture, or browse all GATE CSE PYQs.

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Instruction Set and Addressing Modes in GATE CSE

Instruction Set and Addressing Modes has 19 GATE CSE PYQs across 15 papers from 2011 to 2026. 2 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2014 Set 1.

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