reveal.js

# Binary Numbers and Branching

---

CS 130 // 2025-09-08

# Announcements

## Tutoring Lab is Open

- Cowles Library 201
 - Sundays - Wednesdays 6-9pm
 - Please be understanding if they're not always able to help with CS 130

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# Review

#### Assignment 1 due today

- [Assignment 1](../../assignments/assignment-1/): Write a program that interacts with the user and performs some kind of computation based on their input
- Find other syscall codes in Figure B.9.1 of the textbook

## System Calls

- We can make **system calls** to have the system perform things like input and output
- Put the system call code in `$v0`
- Put argument in `$a0` (and maybe `$a1` if needed)

#### Output a string

- a 4 in `$v0` means *print a string* 
- **address** of the string should be in `$a0`
- `la` means *load address* 
  - contrast with `lw` - use when you want the data *at the address* not the address itself, so use `lw` if you want to print an int

```mips
.data

message: .asciiz "Hello!"

.text

li $v0, 4 #4 is the code for printing a string
la $a0, message #the argument for the syscall
syscall
```

#### User Input

- a 5 in `$v0` means *read an integer* 
- whatever the user types gets put into `$v0` during the syscall

```mips
.data

prompt: .asciiz "Enter an integer:"

.text

li $v0, 4 #4 is the code for printing a string
la $a0, prompt #the argument for the syscall
syscall

li $v0, 5 #5 is the code for reading an integer
syscall
```

# Logical Operations

## Boolean values
- Suppose I create a `bool` variable in Python:
    ```py
    b = True
    ```
- 
 How many bits of memory were just allocated?
    + 
 An entire word!
    + 
 `b` is a **memory address** that "points to" `True`

## Logical operator investigation

Before executing: guess what you think `$t0`-`$t5` will be

Execute it: were you right?

Is this how `and` and `or` behave in Python?
</div>
<div>

```mips
   .text

li $s0, 0
   li $s1, 1
   li $s2, 2
   li $s3, 3
   
   and $t0, $s0, $s1
   or $t1, $s0, $s1
   andi $t2, $s1, 1
   ori $t3, $s1, 0
   
   or $t4, $s1, $s2
   and $t5, $s2, $s3
```

</div>

# Binary Numbers

# CS Jokes

![Only 10 types of people shirt](/Fall2025/CS130/assets/images/shirt10typesOfPeople.jpg)

Source: https://www.amazon.com/Types-People-understand-Binary-T-Shirt/dp/B07PSPLSC9

## Let's talk about how counting works

![Odometer rollover](/Fall2025/CS130/assets/images/Odometer_rollover.jpg)

How do you count if you only have two digits?

## Counting in Binary
- CPUs compute in **binary** using the contrast of low/high voltages to mean 0 and 1 - the two _binary digits_ or **bits**
- So how do we encode **numbers** in binary?

## Base 10 (AKA Decimal)

- When we write 437 we usually mean base 10 - the number system with 10 digits

- Can also write it as $437_\text{ten}$

- $437_\text{ten}$ means

`$$(4\cdot 100)+(3\cdot 10)+(7\cdot 1)$$`

`$$(4\cdot 10^2)+(3\cdot 10^1)+(7\cdot 10^0)$$`

## Base 2 (AKA Binary)

$1101_\text{two}$ means

`$$(1\cdot 8)+(1\cdot 4)+(0\cdot 2)+(1\cdot 1)$$`

`$$(1\cdot 2^3)+(1\cdot 2^2)+(0\cdot 2^1)+(1\cdot 2^0)$$`

### Demo: Let's convert numbers to different bases

- $110110101_\text{two}$

- $437_\text{ten}$

### Exercise: Practice with Binary
- Convert the following number into decimal:
    + $1011010_\text{two}$
- Convert the following decimal number into binary:
    + $277_\text{ten}$

### 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

### 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)
```