Suppose a computer has 32-bit instructions. The instruction set consists of 120 different instructions. All instructions have an addresses must be a register direct address, and opcode and two address fields (allowing for two addresses). The first of these the second must be a memory address. Expanding opcodes are not used. The machine has 16 registers. largest memory space that can be addressed by this computer? What's the size of the Assume byte addressable memory.

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### Understanding Instruction Set Architecture and Memory Addressing in Computers

**Scenario:**
Suppose a computer has 32-bit instructions. The instruction set consists of 120 different instructions. All instructions have an opcode and two address fields (allowing for two addresses). The first of these addresses must be a register direct address and the second must be a memory address. Expanding opcodes are not used. The machine has 16 registers.

**Question:**
What is the size of the largest memory space that can be addressed by this computer? Assume byte-addressable memory.

**Explanation:**

1. **Instruction Format:**
   - A 32-bit instruction can be broken down into different parts: the opcode and the address fields.
   
2. **Opcode:**
   - There are 120 different instructions, so we need enough bits to encode all of them.
   - The number of bits required to represent 120 instructions is log2(120) ≈ 7 bits (since 2^7 = 128, which covers 120 instructions).

3. **Register Direct Address:**
   - The machine has 16 registers; thus, each register can be addressed using log2(16) = 4 bits.

4. **Memory Address:**
   - The remaining bits in the 32-bit instruction will be used for the memory address field.
   - Total bits used so far: 7 bits (opcode) + 4 bits (register address) = 11 bits.
   - Remaining bits for memory address: 32 bits - 11 bits = 21 bits.

5. **Memory Addressing:**
   - With 21 bits available for memory addresses, the maximum addressable memory space can be calculated.
   - The largest memory space = 2^21 bytes = 2,097,152 bytes = 2 MB (Megabytes).

Therefore, the size of the largest memory space that can be addressed by this computer is **2 MB**.
Transcribed Image Text:### Understanding Instruction Set Architecture and Memory Addressing in Computers **Scenario:** Suppose a computer has 32-bit instructions. The instruction set consists of 120 different instructions. All instructions have an opcode and two address fields (allowing for two addresses). The first of these addresses must be a register direct address and the second must be a memory address. Expanding opcodes are not used. The machine has 16 registers. **Question:** What is the size of the largest memory space that can be addressed by this computer? Assume byte-addressable memory. **Explanation:** 1. **Instruction Format:** - A 32-bit instruction can be broken down into different parts: the opcode and the address fields. 2. **Opcode:** - There are 120 different instructions, so we need enough bits to encode all of them. - The number of bits required to represent 120 instructions is log2(120) ≈ 7 bits (since 2^7 = 128, which covers 120 instructions). 3. **Register Direct Address:** - The machine has 16 registers; thus, each register can be addressed using log2(16) = 4 bits. 4. **Memory Address:** - The remaining bits in the 32-bit instruction will be used for the memory address field. - Total bits used so far: 7 bits (opcode) + 4 bits (register address) = 11 bits. - Remaining bits for memory address: 32 bits - 11 bits = 21 bits. 5. **Memory Addressing:** - With 21 bits available for memory addresses, the maximum addressable memory space can be calculated. - The largest memory space = 2^21 bytes = 2,097,152 bytes = 2 MB (Megabytes). Therefore, the size of the largest memory space that can be addressed by this computer is **2 MB**.
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