Arithmetic

# Arithmetic

Week 5

NOTES:
Closed laptops _unless_ we are doing an exercise.

---

## Review

![](https://media.giphy.com/media/v1.Y2lkPWVjZjA1ZTQ3anplbWR4NW5sbDkzMjdldXRpNDJnNjZpa3J3dW12aXUyNXc5c3ZnaSZlcD12MV9naWZzX3NlYXJjaCZjdD1n/nTZt1E0IM8sKSEVirG/giphy.gif)

What is a **condition**?

Something that happens based on `True` or `False`

`=` vs `==`?

- Assigns a value 
- Compares two values

What are the three parts of an `if`?

1. "if" keyword 
2. A true/false condition 
3. A colon : then an indented block

What does `else` do?

The other path — runs when the `if` was `False`

What does `elif` do?

Checks another condition when the previous one was `False`

What is wrong with this code?

```py
if x == 5
    print("x is 5")
```

Missing `:`

What is wrong with this code?

```py
if x = 5:
    print("x is 5")
```

Assignment operator (`=`) instead of equality operator (`==`)

What is wrong with this code?

```py
if x == 5:
    print("x is 5")
        print("Conditions are cool!")
```

Invalid indentation

---

## Computing Machines

**Compute** = to calculate, to count

A **computer** is a machine that does math

NOTE: From Latin _computare_ — "to count, to sum up." The name is literal.

The first computers were **people**

"Computer" was a job title

![NACA human computers at work](https://upload.wikimedia.org/wikipedia/commons/0/06/Human_computers_-_Dryden.jpg?utm_source=en.wikipedia.org&utm_campaign=imageinfo&utm_content=thumbnail_unscaled)

NOTE: 1940s–60s. Teams (often women) computed by hand for astronomy, the census, ballistics, and NASA. _Hidden Figures_ is this story.

People are slow and make mistakes

So we built **machines** to compute for us

![Pascaline mechanical calculator](https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Arts_et_Metiers_Pascaline_dsc03869.jpg/1280px-Arts_et_Metiers_Pascaline_dsc03869.jpg)

Pascaline (1642) — gears that add and subtract

NOTE: Blaise Pascal built it for his father's tax work. Still just arithmetic.

![Babbage Difference Engine](https://upload.wikimedia.org/wikipedia/commons/8/8b/Babbage_Difference_Engine.jpg?utm_source=en.wikipedia.org&utm_campaign=imageinfo&utm_content=thumbnail_unscaled)

Babbage's Difference Engine (1800s) — a steam-era calculator

NOTE: Charles Babbage designed it to print math tables without human error. Ada Lovelace wrote about programming a later design of his.

![ENIAC](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/ENIAC_Penn1.jpg/1280px-ENIAC_Penn1.jpg)

ENIAC (1945) — electronic, built to **crunch numbers**

First general-purpose electronic computer

NOTE: Ballistics tables for the U.S. Army. 5,000 additions per second. Room-sized. Same job as the human computers, just faster.

We call "general-purpose electronic computers" just "computers"

Games, photos, websites, AI — still math underneath

The CPU's core is an **ALU**

Arithmetic Logic Unit: add, subtract, compare

NOTE: Week 2: everything is binary numbers. Text, images, sound are numbers. The ALU is the part that actually does the math.

---

## Basic Math

| Operator | Meaning |
| --- | --- |
| `+` | add |
| `-` | subtract |
| `*` | multiply |
| `/` | divide |

`+` add

```py
print(3 + 2)
```

```txt
5
```

`-` subtract

```py
print(3 - 2)
```

```txt
1
```

`*` multiply

```py
print(3 * 2)
print(3 * 4.0)
```

```txt
6
12.0
```

`*` gives a **float** if at least one of the **operands** is a float

`/` divide

```py
print(3 / 2)
print(3 / 3)
```

```txt
1.5
1.0
```

`/` always gives a **float**

What is the output of each line?

```py
print(10 + 3)  # 1
print(10 - 3)  # 2
print(10 * 3)  # 3
print(10 / 3)  # 4
```

- 13 
- 7 
- 30 
- 3.333...

---

## More Math

| Operator | Meaning |
| --- | --- |
| `//` | integer division |
| `%` | remainder (modulo) |
| `**` | exponent (power) |

`//` integer division

Drops the remainder

```py
print(7 / 2)
print(7 // 2)
```

```txt
3.5
3
```

`%` remainder (modulo)

```py
print(7 % 2)
```

```txt
1
```

`**` exponent (power)

```py
print(3 ** 2)
```

```txt
9
```

What is the output of each line?

```py
print(11 // 4)  # 1
print(11 % 4)   # 2
print(2 ** 3)   # 3
```

1. 2 
2. 3 
3. 8

Modulo is useful for **even vs odd**

```py [2]
number = int(input("Enter a number: "))
is_even = number % 2 == 0
if is_even:
    print(number, "is even")
else:
    print(number, "is odd")
```

NOTE: Even numbers have remainder 0 when divided by 2.

Example: calculating **times**

```py
duration = 90
hours    = minutes // 60
minutes  = duration % 60
print(f'{hours} hr and {minutes} min')
```

---

## Order of Operations

Same order as math class

1. Parentheses: `()`
2. Exponents `**`
3. Multiply & divide: `* / // %`
4. Add & subtract: `+ -`

```py
print(2 + 3 * 4)    # 14, not 20
print((2 + 3) * 4)  # 20
```

What is the output?

```py
print(2 ** 3 + 1)
```

`9` — exponent first, then add

What is the output?

```py
print(10 - 6 / 2)
```

`7.0` — divide first, then subtract

When in doubt, use parentheses

```py
print((10 - 6) / 2)  # 2.0
```

---

## Assignment Shorthand

`=` stores a value in a variable

```py
score = 0
```

To change a value, use it on both sides

```py
score = 0
score = score + 1
print(score)  # 1
```

Shorthand: do the math **and** assign

| Long way | Short way |
| --- | --- |
| `score = score + 1` | `score += 1` |
| `score = score - 1` | `score -= 1` |
| `score = score * 2` | `score *= 2` |
| `score = score / 2` | `score /= 2` |

NOTE: Students already used `+=` on the quiz.

What's wrong here?

```py []
count += 1
```

`count` was never assigned a starting value

```py []
count = 0
count += 1
```

What is the result?

```py
some_number = 8
some_number *= 2
```

```txt
16
```

What is the result?

```py
some_number = 90
some_number //= 2
```

```txt
45
```

What is the result?

```py
some_number = 90
some_number %= 2
```

```txt
0
```

---

## String Math

`+` on strings **concatenates** (joins)

```py
print("10" + "3")
print("Hello, " + "World!")
```

```txt
103
Hello, World!
```

What's wrong here?

```py
a = input("First number: ")
b = input("Second number: ")
print(a + b)
```

`input()` returns strings, so `+` concatenates

```txt
First number: 10
Second number: 3
103
```

Convert first, then do math

```py
a = float(input("First number: "))
b = float(input("Second number: "))
print(a + b)
```

```txt
First number: 10
Second number: 3
13.0
```

NOTE: `int()` for whole numbers, `float()` for decimals. `float("10")` works. `int("10.5")` does not.

`*` on a string **repeats** it

```py
print("ha" * 3)
print("-" * 10)
```

```txt
hahaha
----------
```

What is the output of each line?

```py
print("2" + "2")  # 1
print(2 + 2)      # 2
print("2" * 3)    # 3
```

- 22 
- 4 
- 222

---

## Exercise

Create a program that does the following:

1. Ask user for a word or phrase
2. Compute the word length using `len()`
3. Print word in frame, computed with math

!["foobar" in ASCII art](/2026/computer-science/images/foobar-ascii-art.png)

```py
word = input("Type a word: ")
word_width = len(word)

line   = '-' * (word_width + 8)
spaces = ' ' * (word_width + 8)

print(f"O{line}O")
print(f"|{spaces}|")
print(f"|    {word}    |")
print(f"|{spaces}|")
print(f"O{line}O")
```

---

![Jimmy Fallon thats it](https://media4.giphy.com/media/v1.Y2lkPTc5MGI3NjExd2NmamM3NmR2c3RtenR3bGV5dnR1MnNyM3BzNnh3ZGNwYTFyZ2V6YyZlcD12MV9pbnRlcm5hbF9naWZfYnlfaWQmY3Q9Zw/uSZQ6WPIcpouUEpNTe/giphy.gif)