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A processor has $70$ distinct instructions and $46$ general purpose registers. A $32$-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is $Z$. Compute the smallest positive value of the difference $2^p - Z$, where p is some non-negative integer _________
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+1 vote
For OPCODE part at least 7 bits are needed and for Register part at least 6 bits are needed. So $7+6+6+Z=32$ gives $Z=13$ bits.
So smallest value of $2^p-13= 2^4-13=3$ for $p=4$.
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