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Suppose a 32-bit instruction takes the two following format: OPCODE DR SR1 SR2 UNUSED ОРСODE DR SR1 IMM If there are 140 opcodes and 128 registers, a) What is the size (in bits) of each field? b) What is the range of IMM field?

Suppose a 32-bit instruction takes the two following format: OPCODE DR SR1 SR2 UNUSED ОРСODE DR SR1 IMM If there are 140 opcodes and 128 registers, a) What is the size (in bits) of each field? b) What is the range of IMM field?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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### 32-bit Instruction Format and Field Calculation In this lesson, we will discuss the format of a 32-bit instruction and the sizes of its fields based on the given number of opcodes and registers. #### Instruction Formats Suppose a 32-bit instruction takes one of the two following formats: 1. **Format 1:** ``` OPCODE DR SR1 SR2 UNUSED ``` 2. **Format 2:** ``` OPCODE DR SR1 IMM ``` Here, - **OPCODE** represents the operation code. - **DR** (Destination Register) is the register where the result will be stored. - **SR1** (Source Register 1) is the first source register. - **SR2** (Source Register 2) is the second source register. - **UNUSED** represents unused bits in the instruction. - **IMM** (Immediate) represents an immediate value used in the instruction. #### Field Size Calculation Given: - **Number of opcodes:** 140 - **Number of registers:** 128 We need to calculate: - The size (in bits) of each field. - The range of the IMM field. **a) Size (in bits) of each field:** 1. **OPCODE:** - To represent 140 different opcodes, we need sufficient bits to accommodate all possible values. - The number of bits required is given by \(\lceil \log_2(140) \rceil\). - \(\log_2(140) \approx 7.14\rightarrow \lceil 7.14 \rceil = 8\) bits. 2. **Registers (DR, SR1, SR2):** - To represent 128 different registers, we need sufficient bits to accommodate all possible values. - The number of bits required is given by \(\lceil \log_2(128) \rceil\). - \(\log_2(128) = 7\) bits. **b) Range of IMM field:** - Since the total instruction length is 32 bits, we can calculate the size of the IMM field. - The first format uses OPCODE, DR, SR1, SR2, and UNUSED fields. - OPCODE: 8 bits - DR: 7 bits
Transcribed Image Text:### 32-bit Instruction Format and Field Calculation In this lesson, we will discuss the format of a 32-bit instruction and the sizes of its fields based on the given number of opcodes and registers. #### Instruction Formats Suppose a 32-bit instruction takes one of the two following formats: 1. **Format 1:** ``` OPCODE DR SR1 SR2 UNUSED ``` 2. **Format 2:** ``` OPCODE DR SR1 IMM ``` Here, - **OPCODE** represents the operation code. - **DR** (Destination Register) is the register where the result will be stored. - **SR1** (Source Register 1) is the first source register. - **SR2** (Source Register 2) is the second source register. - **UNUSED** represents unused bits in the instruction. - **IMM** (Immediate) represents an immediate value used in the instruction. #### Field Size Calculation Given: - **Number of opcodes:** 140 - **Number of registers:** 128 We need to calculate: - The size (in bits) of each field. - The range of the IMM field. **a) Size (in bits) of each field:** 1. **OPCODE:** - To represent 140 different opcodes, we need sufficient bits to accommodate all possible values. - The number of bits required is given by \(\lceil \log_2(140) \rceil\). - \(\log_2(140) \approx 7.14\rightarrow \lceil 7.14 \rceil = 8\) bits. 2. **Registers (DR, SR1, SR2):** - To represent 128 different registers, we need sufficient bits to accommodate all possible values. - The number of bits required is given by \(\lceil \log_2(128) \rceil\). - \(\log_2(128) = 7\) bits. **b) Range of IMM field:** - Since the total instruction length is 32 bits, we can calculate the size of the IMM field. - The first format uses OPCODE, DR, SR1, SR2, and UNUSED fields. - OPCODE: 8 bits - DR: 7 bits
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