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# MIPS Machine Code

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CS 130 // 2025-09-24

# Review

## Two's Complement
- Most computers use **two's complement** to encode signed integer values
- What is it exactly?
    + 
 Non-negative numbers are represented as usual<br>$0000$, $0011$, $0110$
    + 
 To negate a number, you do the following:
        1. Flip all the bits: $0\rightarrow 1$ and $1\rightarrow 0$
        2. Add 1 to the result
    + 
 $0000$, $1101$, $1010$

## Exercise
### Two's Complement Practice
- Convert each of the following numbers to decimal:

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- $1111\\;1111\\;1111\\;1111\\;1111\\;1111\\;1111\\;1111$
- $1111\\;1111\\;1111\\;1111\\;1111\\;1111\\;1110\\;0101$
- $0000\\;0000\\;0000\\;0000\\;0000\\;0000\\;0000\\;0101$

## Demo: Adding two binary numbers

* Let's use some 8-bit binary numbers 
<pre>
      0010 0011       0001 1000
    + 1111 0100     - 0011 0110
    ------------    ------------
</pre>

## Exercise

* Using 8-bit binary numbers, show how to compute 
    - 68 - 55
    - 20 + 40
    - 30 - 127
    - -10 + -3

# MIPS Machine Code

## MIPS Machine Code
- Each MIPS instruction is encoded in 32-bits
    + 
 `add` `$t0`, `$s1`, `$s2`
    + 
 000000 10001 10010 01000 00000 100000

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![R-Type Instruction](/Fall2025/CS130/assets/images/COD/r-type-instruction.png)

## R-Type Instructions
![R-Type Instruction](/Fall2025/CS130/assets/images/COD/r-type-instruction.png)

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1. 
 `op` (6 bits): Opcode
2. 
 `rs` (5 bits): First operand register
3. 
 `rt` (5 bits): Second operand register
4. 
 `rd` (5 bits): Destination register (result)
5. 
 `shamt` (5 bits): Shift amount
6. 
 `funct` (6 bits): Function code

## I-Type Instructions
![I-Type Instruction](/Fall2025/CS130/assets/images/COD/i-type-instruction.png)

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1. `op` (6 bits): Opcode
2. `rs` (5 bits): First operand register
3. `rt` (5 bits): Second operand register
4. 
 `data` (16 bits): Constant or address

## Exercise

- Use Mars to figure out how each of the following is represented in bits (convert from hex!).
```mips
add $t2, $t1, $t0
sub $t2, $t1, $t0
addi $t0, $t0, 3
```
- What are the opcodes for `add`, `sub`, and `addi`?

## R-Type VS I-Type
- Why do we need the I-type? Why not just implement `addi`, `lw`, and `sw` using the R-type format?
    + 
 Allows us to specify larger addresses and constants
    + 
 $2^5 = 32$ and $2^{16} = 65536$

# Shift Instructions

## Shifting investigation

Execute it: what do `sll` and `srl` do?

What happens if you shift an odd number?

Are these R-Type or I-Type instructions?
</div>
<div>

```mips
.text

li $s0, 16

#shift left logical
sll $t0, $s0, 1
sll $t1, $s0, 2

#shift right logical
srl $t2, $s0, 2
```

</div>