Please provide a step by step solution of the above question(for each part). The

Question

Please provide a step by step solution of the above question(for each part).

The word-addressable memory unit of a computer has 256K words of 32 bits each. The computer has an instruction format with 4 fields: an opcode field; a mode field to specify 1 of 7 addressing modes: a register address field to specify 1 of 60 registers: and a memory address field. Assume an instruction is 32 bits long. Answer the following: How large must the mode field be? How large must the register field be? How large must the address field be? How large is the opcode field?

Explanation / Answer

a. The system has 1 to 7 modes, i.e 7 different states. To represent 7 states we need at least log27 bits or 2.8 bits, but we cannot have 0.8 bit, so we need to round up to 3 bits.

b. Similarly, register field must be log260 wide or 5.9 bits wides. So we need to round up to 6 bits.

c. The system can address 256K words, therefore we need log2(256*1024) bits or 18bits are required for address field

d. We also know that the instructions are 32bits long.
       out of 32 bits 3bits are required for mode selection, 6bits for register addressing, and 18bits to address memory
      therefore out of 32bits at least 27bits are already used up
      so opcode field can be at most 5bits long.

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