GATE 2024 CS2 Q.57: solution and answer

GATE 2024 · CS2Q.57 · 2 marks · NAT

A processor with 16 general purpose registers uses a 32-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two register operand fields, and a 16-bit scalar field. If 8 addressing modes are to be supported, the maximum number of unique opcodes possible for every addressing mode is ____

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Answer and solution

ANSWER

The maximum number of unique opcodes possible for every addressing mode is 32.

Official answer: 32Source: Official answer key, GATE 2024 CS2 (IISc Bengaluru)

Total instruction length is fixed at 32 bits, shared among the opcode field, addressing-mode field, two register-operand fields, and a 16-bit scalar (immediate) field.
16 general purpose registers require $⌈ lo g_{2} 16 ⌉ = 4$ bits to encode each register operand; with two register-operand fields this uses $2 \times 4 = 8$ bits.
The scalar (immediate) field is given directly as 16 bits.
Bits used so far (both register fields plus the scalar field) $= 8 + 16 = 24$ bits.
Bits remaining for the opcode field and the addressing-mode field together $= 32 - 24 = 8$ bits.
8 addressing modes require $⌈ lo g_{2} 8 ⌉ = 3$ bits for the addressing-mode field.
Bits left over for the opcode field $= 8 - 3 = 5$ bits.
Maximum number of unique opcodes possible for every addressing mode $= 2^{5} = 32$ .

KEY IDEA

Total instruction width is fixed at 32 bits; every field that is spelled out numerically (register fields, scalar field, addressing-mode field) eats into that budget, and whatever bits remain form the opcode field, whose size determines the count of distinct opcodes as $2^{opcode bits}$ .

WATCH OUT FOR

Forgetting to subtract the addressing-mode field bits before computing the opcode field width, i.e. taking opcode field = 32 − 24 = 8 bits directly (giving 2^8 = 256) instead of first removing the 3 bits needed to encode 8 addressing modes.

From the GATE 2024 CS2 paper. Every question of this paper · Download the full paper · All 11 Instructions & addressing questions, with notes

GATE 2024 CS2 Q.57: solution and answer

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