reveal.js

# Branching

---

CS 130 // 2025-09-10

# Hexadecimal

### Base 16 (AKA Hexadecimal)

- Hexadecimal is base 16
- digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- 5C means

`$$(5\cdot 16)+(12\cdot 1)$$`

- Easy to convert back and forth from binary
- Used as *shorthand* for binary

### Counting in Binary/Hexadecimal

<table>
  <tbody>
    <tr> <th>Decimal</th> <th>Binary</th><th>Hex</th></tr>
    <tr> <td>0</td> <td>0000</td> <td>0</td></tr>
    <tr> <td>1</td> <td>0001</td> <td>1</td></tr> 
    <tr> <td>2</td> <td>0010</td><td>2</td></tr>
    <tr> <td>3</td> <td>0011</td> <td>3</td></tr>
    <tr> <td>4</td> <td>0100</td><td>4</td></tr>
    <tr> <td>5</td> <td>0101</td><td>5</td></tr>
    <tr> <td>6</td> <td>0110</td><td>6</td></tr>
    <tr> <td>7</td> <td>0111</td><td>7</td></tr>
    <tr> <td>8</td> <td>1000</td> <td>8</td></tr>
  </tbody>
</table>

</div>
<div>

<table>
  <tbody>
    <tr> <th>Decimal</th> <th>Binary</th><th>Hex</th></tr>
    <tr> <td>9</td> <td>1001</td> <td>9</td></tr>
    <tr> <td>10</td> <td>1010</td><td>A</td></tr>
    <tr> <td>11</td> <td>1011</td> <td>B</td></tr>
    <tr> <td>12</td> <td>1100</td><td>C</td></tr>
    <tr> <td>13</td> <td>1101</td><td>D</td></tr>
    <tr> <td>14</td> <td>1110</td><td>E</td></tr>
    <tr> <td>15</td> <td>1111</td><td>F</td></tr>
    <tr> <td>16</td> <td>0001 0000</td><td>10</td></tr>
    <tr> <td>17</td> <td>0001 0001</td><td>11</td></tr>
  </tbody>
</table>

</div>
</div>

### Exercise: Exploring in Mars
  
- Open up Mars and create a `.asm` file 
- Put the number 302 in your data section
- How does Mars display that in Hex?
- What is the Binary equivalent?

### Exercise: Convert back and forth
  
- Convert the following binary number into hex
  - $\text{1111 1010 0001 1011 0100 1110 0010 0011}_\text{two}$
- Convert the following hexadecimal number into binary
  - $\text{00FF33AA}_\text{hex}$

# Conditionals

## Branching
- **Branching** allows MIPS programs to skip around to different parts of the program
- Useful for
    - conditional statements (if, if-else, etc.)
    - loops

- continue executing at the line labeled `my_label`
```mips
b my_label
#...
my_label:
```
- 
 continue executing at the line labeled `my_label` if `$s0` and `$s1` are equal
```mips
beq $s0, $s1, my_label
```
- 
 continue executing at the line labeled `my_label` if `$s0` and `$s1` are _not_ equal
```mips
bne $s0, $s1, my_label
```

## Compiling an `if` Statement

```python
    if i == j:
        k = 1

print("The value of k is",k)
```

</div>
<div>

```mips
.data

i: 5
j: 8
k: 0
message: .asciiz "The value of k is "

.text

lw $s0, i
	lw $s1, j
	
	bne $s0, $s1, disp_msg
	li $s2, 1
	sw $s2, k

disp_msg:
	li $v0, 4 #4 is the code for printing a string
	la $a0, message #the argument for the syscall
	syscall 
	
	li $v0, 1 #1 is the code for printing an int
	lw $a0, k #the argument for the syscall
	syscall 
```
<div>

## Exercise

- Run the above program in Mars, observe the output
- Change it so `i` and `j` are equal, run again
- Translate the following Python program into MIPS
```python
    if i == j:
        k = 1
    else:
        k = 2

print("The value of k is",k)
```

## Set on Less Than investigation

Before executing: guess what you think `$t0`-`$t6` will be

Execute it: were you right?

What do `sle` and `sgt` mean? What do they get translated into by the assemler?
</div>
<div>

```mips
.text

li $s1, 2
li $s2, 2
li $s3, 3

#slt: "set on less than"
slt $t0, $s2, $s3
slt $t1, $s1, $s2
slt $t2, $s3, $s2
slti $t3, $s3, 10

#psuedoinstructions
sle $t4, $s1, $s3
sle $t5, $s1, $s2
sgt $t6, $s3, $s2
```

</div>

## Exercise

- Translate the following Python program into MIPS
- This is the same as your previous exercise, except with `i < j` instead of `i == j`
```python
    if i < j:
        k = 1
    else:
        k = 2

print("The value of k is",k)
```

## Compiling a `while` Statement

```python
i = 1
while i != 10:  
   print(i)
   i += 1
```

---

```mips
.text
	li $s0, 1
	li $t0, 10
	
start_loop:
	beq $s0, $t0, done

li $v0, 1 #print integer - no newline after!
	add $a0, $s0, $zero #copy $s0 into $a0
	syscall

addi $s0, $s0, 1
	b start_loop

done:
```

## Exercise

- Translate this into MIPS
- Hint: can you use `slt` here?

```python
sum = 0
i = 0

while i < 10:
    sum = sum + i
    i += 1

print(sum)
```

</div>

## Assignment

- [Assignment 2](../../assignments/assignment-2/)
  - Translate a Python program that has both an if statement and a loop