Finding the maximum number of registers that can be assigned to certain machine?

Question

Finding the maximum number of registers that can be assigned to certain machine?

I am confused on what they are doing here

Can somebody please explain?

Instruction Encoding - Example What is the max number of registers that can be designed in a machine given: 16-bit instructions Num. opcodes 100 * All instructions are (reg, reg) reg (i.e., 2 source operands, 1 destination operand) opcode dest src1 src2 16 bits 1. num opcode bits =log2(100)-7 2. num bits for operands 16-7 9 3, num bits per operand = 9 / 3-3 4. maximum number of registers 2A3 8

Explanation / Answer

here total length of instruction = 16 bits

number of opcodes = 100

value of 100 in binary = 1100100 so it needs 7 bits to store 100 different opcodes

now remaining bits = 16 -7 = 9bits

9 bits can be divided among dest,src1 and src2 registers

9 divided by 3 = 3

so 3 bits each for each of these three registers

7+3+3+3 = 16 bits

opcode = 9 bits dest = 3 bits src1 = 3 bits src2 = 3 bits

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