Exam 2 Review for CECS 341: MIPS
Architecture Concepts
Binary Arithmetic and Two's Complement
Understanding Two's Complement
Two's complement is a method for representing signed integers in binary, allowing for
easy arithmetic operations.
To find the two's complement of a number, invert the bits and add one to the least
significant bit (LSB).
Example: For the number 4 (binary 0000 0100), its two's complement is 1111 1100
(invert bits) + 1 = 1111 1101.
This method simplifies subtraction by converting it into addition, as seen in the problem
of 6 - 4.
In a 32-bit system, the two's complement representation allows for a range of -
2,147,483,648 to 2,147,483,647.
The result of adding a positive number and the two's complement of another will yield
the correct difference.
Binary Subtraction Example
Consider the subtraction of 6 - 4 using binary: 6 is 0000 0110 and 4 is 0000 0100.
The two's complement of 4 is calculated as 1111 1100, and adding this to 6 gives:
0000 0110
1111 1100
-----------------
0000 0010 (which is 2 in decimal).
The values of dcba and zyxw can be derived from the binary addition process, where
dcba represents the two's complement of 4 and zyxw represents the result of the
addition.
The answer for dcba is 1100 (option b) and for zyxw is 0010 (option d).
, MIPS Architecture and Instructions
MIPS Instruction Types
MIPS architecture uses different instruction types: R-type, I-type, and J-type, each
serving specific purposes in data processing.
R-type instructions involve operations on registers, while I-type instructions include
immediate values and memory access.
Example: The instruction 'add
t2,
t2 and
t1.
The 'lw' (load word) and 'sw' (store word) instructions are examples of I-type
instructions that interact with memory.
Understanding the format of these instructions is crucial for decoding and executing
them correctly in the MIPS pipeline.
Each instruction type has specific control signals that dictate the behavior of the
datapath.
Architecture Concepts
Binary Arithmetic and Two's Complement
Understanding Two's Complement
Two's complement is a method for representing signed integers in binary, allowing for
easy arithmetic operations.
To find the two's complement of a number, invert the bits and add one to the least
significant bit (LSB).
Example: For the number 4 (binary 0000 0100), its two's complement is 1111 1100
(invert bits) + 1 = 1111 1101.
This method simplifies subtraction by converting it into addition, as seen in the problem
of 6 - 4.
In a 32-bit system, the two's complement representation allows for a range of -
2,147,483,648 to 2,147,483,647.
The result of adding a positive number and the two's complement of another will yield
the correct difference.
Binary Subtraction Example
Consider the subtraction of 6 - 4 using binary: 6 is 0000 0110 and 4 is 0000 0100.
The two's complement of 4 is calculated as 1111 1100, and adding this to 6 gives:
0000 0110
1111 1100
-----------------
0000 0010 (which is 2 in decimal).
The values of dcba and zyxw can be derived from the binary addition process, where
dcba represents the two's complement of 4 and zyxw represents the result of the
addition.
The answer for dcba is 1100 (option b) and for zyxw is 0010 (option d).
, MIPS Architecture and Instructions
MIPS Instruction Types
MIPS architecture uses different instruction types: R-type, I-type, and J-type, each
serving specific purposes in data processing.
R-type instructions involve operations on registers, while I-type instructions include
immediate values and memory access.
Example: The instruction 'add
t2,
t2 and
t1.
The 'lw' (load word) and 'sw' (store word) instructions are examples of I-type
instructions that interact with memory.
Understanding the format of these instructions is crucial for decoding and executing
them correctly in the MIPS pipeline.
Each instruction type has specific control signals that dictate the behavior of the
datapath.
