Finding maximum number of register counts from instruction size, op-code size, and number of operands

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I've been trying to wrap my head around how to achieve the answer. I'd like to say I did my own research but either I'm not searching the right questions or I'm blind. Can someone please explain the logic behind finding the answer? I am at a loss.

Enter the register counts:

16 bit instruction, 5-bit opcode, maximum register count with 2 operands

16 bit instruction, 8-bit opcode, maximum register count with 2 operands

instruction-set computer-science cpu-registers cpu-architecture
1 Answers

It's just arithmetic. 16 bits total, 5 are used for the opcode, leaving 11. Dividing 11 by two shows that if you need two operands, each one can have at most 5 bits to represent it, and you'll have 1 bit left over for something else. With 5 bits you can address 2^5=32 registers.

Now you do the other one.

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