Gate2020 cs Q41

41A processor has 64 registers and uses 16-bit instruction format. It has two type instruction: 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 _____.

Note – Numerical Type question

Option : A
Explanation :

⇒ # of instruction possible = 2⁴ = 16
∴ No. of free opcodes = 16 – x
Let x is number of R-type instruction exist
∴ No. of I-type instruction possible = (16 – x) * 2²
8 = 64 – 4x
4x = 64 – 8 = 56
x = 14

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