We Know $rs= 0x1101 0000, The Instruction Ori $rt,$rs,0x6789 Is Executed, What Is In $rt (in Hex)?
Understanding how MIPS assembly instructions work is essential for anyone studying computer architecture or low-level programming. In this article, we analyze a specific instruction execution scenario: given that register $rs contains 0x11010000, and the instruction Ori $rt, $rs, 0x6789 is executed, what will be the value stored in register $rt? We will explore the details step-by-step, including the binary and hexadecimal representations, the bitwise OR operation, and how the final value in $rt is derived.
Understanding the Context of the Instruction
What is the Ori Instruction?
The Ori instruction in MIPS assembly language is a logical OR immediate operation. It performs a bitwise OR between the contents of a source register ($rs) and an immediate value, then stores the result in a target register ($rt). Its general syntax is:```assembly
Ori $rt, $rs, immediate
```
This instruction is commonly used to set specific bits in a register without affecting others.
Given Data and Goal
- The value in register $rs is 0x11010000.
- The immediate value to OR with is 0x6789.
- The question: after executing `Ori $rt, $rs, 0x6789`, what is the hexadecimal value stored in $rt?
Converting Values to Binary for Bitwise Operations
Register $rs Value in Hex and Binary
The value in $rs is:```hex
0x11010000
```
Converting to binary:
- 0x1 = 0001
- 0x1 = 0001
- 0x0 = 0000
- 0x1 = 0001
- 0x0 = 0000
- 0x0 = 0000
- 0x0 = 0000
- 0x0 = 0000
Putting it all together:
```
0x11010000 = 0001 0001 0000 0001 0000 0000 0000 0000
```
For clarity, in a 32-bit binary:
```
0001 0001 0000 0001 0000 0000 0000 0000
```
Immediate Value in Hex and Binary
The immediate is:```hex
0x6789
```
Converting to binary:
- 0x6 = 0110
- 0x7 = 0111
- 0x8 = 1000
- 0x9 = 1001
Concatenate:
```
0x6789 = 0110 0111 1000 1001
```
Since the immediate is a 16-bit value, in 32-bit register operations, it's zero-extended to 32 bits:
```
0000 0000 0000 0000 0110 0111 1000 1001
```
Final binary for immediate:
```
0000 0000 0000 0000 0110 0111 1000 1001
```
Performing the Bitwise OR Operation
Aligning the Binary Values
- $rs: 0001 0001 0000 0001 0000 0000 0000 0000
- Immediate (zero-extended): 0000 0000 0000 0000 0110 0111 1000 1001
Bitwise OR Process
The OR operation compares each bit position; if either bit is 1, the result is 1.Step-by-step:
| Bit position | $rs bit | Immediate bit | Result bit |
|----------------|----------|----------------|------------|
| 31 | 0 | 0 | 0 |
| 30 | 0 | 0 | 0 |
| 29 | 0 | 0 | 0 |
| 28 | 1 | 0 | 1 |
| 27 | 0 | 0 | 0 |
| 26 | 0 | 0 | 0 |
| 25 | 1 | 0 | 1 |
| 24 | 0 | 0 | 0 |
| 23 | 0 | 0 | 0 |
| 22 | 0 | 0 | 0 |
| 21 | 0 | 0 | 0 |
| 20 | 0 | 0 | 0 |
| 19 | 0 | 0 | 0 |
| 18 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 |
| 15 | 0 | 0 | 0 |
| 14 | 0 | 0 | 0 |
| 13 | 1 | 0 | 1 |
| 12 | 0 | 0 | 0 |
| 11 | 0 | 0 | 0 |
| 10 | 0 | 0 | 0 |
| 9 | 0 | 0 | 0 |
| 8 | 0 | 0 | 0 |
| 7 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 |
| 5 | 0 | 1 | 1 |
| 4 | 0 | 1 | 1 |
| 3 | 0 | 1 | 1 |
| 2 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
Now, constructing the resulting binary value:
```
0001 0001 0000 0001 0110 0111 1000 1001
```
Converted back to hexadecimal:
- Groupings:
| Binary Group | Hex Digit |
|----------------|------------|
| 0001 | 1 |
| 0001 | 1 |
| 0000 | 0 |
| 0001 | 1 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
- Final value in hex:
```hex
0x11016789
```
Conclusion: Final Value in $rt
After executing the instruction `Ori $rt, $rs, 0x6789`, the register $rt will contain the value:
```hex
0x11016789
```
This value results from performing a bitwise OR between the original $rs value (0x11010000) and the immediate (0x6789), with the operation extended to 32 bits.
Summary of Key Points
- The Ori instruction performs a bitwise OR between a register and an immediate value.
- Hexadecimal values can be converted into binary to visualize bitwise operations.
- Zero extension of the 16-bit immediate ensures proper alignment during the OR operation.
- The final register value is obtained by OR-ing each corresponding bit of the source register and the immediate.
- In this specific case, the result is 0x11016789.
Understanding such operations is fundamental in low-level programming and computer architecture, especially for tasks involving bit manipulation, hardware control, and optimization of assembly code.
