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Questions and Answers
What is the first step in negating a two's complement binary number?
What is the first step in negating a two's complement binary number?
What must be added to the inverted representation of a two's complement number to obtain its negation?
What must be added to the inverted representation of a two's complement number to obtain its negation?
Which of the following formats is NOT included in the MIPS format?
Which of the following formats is NOT included in the MIPS format?
In the negation process of a two's complement number, what does 'x̅' represent?
In the negation process of a two's complement number, what does 'x̅' represent?
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Which operation is associated with the I-Format in MIPS architecture?
Which operation is associated with the I-Format in MIPS architecture?
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What can be concluded if the sum of a number and its inverted representation equals -1?
What can be concluded if the sum of a number and its inverted representation equals -1?
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What is the result of adding a two's complement number to its negated form?
What is the result of adding a two's complement number to its negated form?
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Study Notes
Computer Architecture CS 320
- Course taught by Dr. Khaled El Helow
- Course offered by Integrated Thebes Institutes, Thebes Higher Institute of Computer & Management Sciences
Lecture 4: MIPS Format
- Focuses on the MIPS instruction format
Review of Binary Numbers
- Computers use binary digits (bits) in base 2 to represent numbers.
- To calculate a number's value in any base, sum each digit multiplied by the corresponding power of the base.
MIPS 32-bit word
- MIPS words are 32 bits long.
- Bits are numbered from right to left (least significant to most significant bit).
- There are 232 possible combinations of 32-bit values.
- The smallest possible value is 0.
- The largest possible value is 232 - 1 = 4,294,967,295.
- Overflow occurs for unsigned numbers if the value exceeds 4,294,967,295.
Two's Complement Numbers
- Negate a two's complement binary number by inverting all bits (0s to 1s and 1s to 0s) and adding 1.
- The sum of a number and its inverse is always 11...11 (all 1s).
- This result represents -1, so inverting and adding 1 to any value gives its negative equivalent.
- Negative numbers have a most significant bit (MSB) of 1. Positive numbers have a MSB of 0.
- For a 32-bit number, each bit's value corresponds to a power of 2. The MSB is multiplied by -231, and other bits are multiplied by appropriate powers of 2.
Range of Signed Numbers (Two's Complement)
- Range of n-bit signed numbers in two's complement is -2n-1 to 2n-1-1.
Converting Between Binary, Decimal, and Hexadecimal
- Numbers can be converted between binary, decimal, and hexadecimal systems.
MIPS Instruction Formats
- R-format (register-oriented) instructions involve operations involving registers.
- I-format (immediate) instructions allow for constants and addresses within the format itself.
- J-format (jump) instructions contain instructions associated with jumps and branches.
MIPS Fields
- op: opcode, specifying the operation.
- rs, rt: source registers.
- rd: destination register.
- shamt: shift amount (for shift instructions).
- funct: function code, further specifying the operation.
Design Considerations
- Instructions often require more bits than what is immediately available.
- This compromise is a key aspect of MIPS instruction design principles. Concise format with efficient encoding.
Load Word (lw) Instruction
- lw instruction loads data words from memory addresses.
- Addresses are 16 bits which allows access to 216 bytes of memory from a specific register.
MIPS Instruction Encoding
- Instructions are encoded according to R-type and I-type formats.
Translating MIPS Assembly Language to Machine Language
- C code can be translated to MIPS assembly and then to machine code (binary).
- The translation involves using the opcode, registers, and addresses.
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