Welcome to Lecture 7:

Nested Lists + Number Representation

Class will start at 10:10.

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In the meantime, we will go around. Tell me your name, where you’re from, & favorite mythical creature.

Today’s Topics

• Announcements
• Review
• Nested lists
• How to represent a board
• Accessing elements of nested list
• Binary numbers
• Hex numbers
• Converting numbers

Announcements

• I’ll post today’s lecture quiz later tonight (worst case Friday)
• Project 2 - Project Party Friday from 2 to 6PM in SDH-200
• Project 2 is due Monday, 7/1
• Reminder: 2 Lab assignments per lab (conceptual AND coding)
• All office hour locations + times are on website
• Any OH after 7PM will be online (hybrid may be offered)
• *Andrew out next week - no OH

Review from Last Lecture

• Higher Order Functions
• We can create our own
• Function that takes in a function as input
• Lambdas
• Temporary, anonymous functions
• We can set variables to functions / lambdas
• Both
• We need to use “call” or “run” to invoke the function
• We need to specify inputs when invoking if the function has inputs

So far with lists, …

• We’ve seen containing numbers, words, symbols
• But lists can also contain functions!

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So far with lists, …

• We’ve seen containing numbers, words, symbols
• But lists can also contain functions!

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• And other lists!

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• Lists can contain any object and any object type! And lists can mix and match data types for each element

Why use Nested Lists?

• Organizing data
• Represent data structures
• Can represent a board with rows and columns
• Can represent an Excel sheet with titles and then data
• Can create different models of data
• Can represent x, y values and coordinates

Representing a Board

• Representing a Tic-Tac-Toe Board game

Representing X, Y Coordinates

• Representing X, Y Coordinates

Guess that Output!

Guess that Output!

Why use Nested Lists?

• Organizing data
• Represent data structures
• Can represent a board with rows and columns
• Can represent an Excel sheet with titles and then data
• Can create different models of data
• Can represent x, y values and coordinates

Representing a Board

• Representing a Tic-Tac-Toe Board game

Representing X, Y Coordinates

• Representing X, Y Coordinates

Guess that Output!

Guess that Output!

Accessing Elements + Lengths

• Outputs the first ROW of nested list
• The row data type is a list!
• To access an entire column (also outputs a list):
• We can use map!
• To access a specific values at row, column:

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• Length of nested list: Outputs the number of rows
• Length of : Outputs the number of columns in row 1

Guess that Output!

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Guess that Output!

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Guess that Output!

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Guess that Output!

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Accessing Columns

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• How can we report all items in column B?

Accessing Columns

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• How can we report all items in column B?

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• Since each element of coordinates is a list, “map” applies the “item 2” function over each element.

Buggy Code. What went wrong?

• I wanted to get a specific “X”

Accessing Row, Columns with Loops!

• This structure gives me a specific non-list element

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• To generalize this, we’ll need NESTED loops!

Code that Function!

• Objective: Create a sum function that takes in a nested list. Outputs the sum of all the values.

Code that Function!

• the sum of all the values.

Code that Function!

• the sum of all the values.

Code that Function!

• Objective: Add a new element to the end of each row. The new element should be the sum of that particular row

Code that Function!

• Objective: Add a new element to the end of each row. The new element should be the sum of that particular row

Code that Function!

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Code that Function!

• Objective: Create a function that finds the maximum number in the nested list.

Code that Function!

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Code that Function!

• Objective: Create a function that finds the maximum number in the nested list. Do this using HOFs. Hint: You will need to find the maximum of each row first.

Code that Function!

Number Representation: Decimal

• The decimal system has 10 digits
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• We can represent the number: 5423
• (5 * 10³ ) + (4 * 10²) + (2 * 10¹) + (3 * 10⁰)
• When we are using the decimal system, we say we are using base 10
• 5423₁₀ means this number is in decimal
• But there are other numerical systems
• We can write any number in any base!

Number Representation: Base 8

• Let’s say I want to represent a base 8 number
• Let’s use 5423 (but it is no longer the same value/number in base 8)
• We can represent the number: 5423₈ in decimal
• (5 * 8³ ) + (4 * 8²) + (2 * 8¹) + (3 * 8⁰)
• (2560) + (512) + (16) + (3)
• = 2835 in decimal!

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Number Representation: Binary

• The “language” of a computer is binary (ex: 011010101), which is base 2
• Computers store data as binary
• Represent data structures as binary
• Images, numbers, text, code, code, etc!
• Let’s convert 1011 from binary to decimal
• (1 * 2³ ) + (0 * 2²) + (1 * 2¹) + (1 * 2⁰)
• (8) + (0) + (2) + (1)
• = 11 in decimal!

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Number Representation: Binary

• Let’s convert 25 from decimal to binary
• First write out the powers of 2
• Keep writing powers of 2 until we reach a number greater than 25
• (2⁵) + (2⁴) + (2³) + (2² ) + (2¹) + (2⁰) =
• (32) + (16) + (8) + (4) + (2) + (1)
• Next, place place a 1 for all the numbers that allow us to sum to 25, and 0 otherwise - left associative!

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Number Representation: Binary

• Let’s convert 25 from decimal to binary
• Next, place place a 1 for all the numbers that allow us to sum to 25, and 0 otherwise - left associative!

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• Final answer is 11001

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Number Representation: Hexadecimal

• Has 16 different digits:
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
• Let’s convert A3C to decimal:
• (10 * 16² ) + (3 * 16¹) + (12 * 16⁰)
• (2560) + (48) + (12)
• = 2620 in decimal

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Number Representation: Hexadecimal

• Has 16 different digits:
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
• Let’s convert 574 to hexadecimal:
• Continuously divide our number by 16, save the remainders
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Number Representation: Hexadecimal

• Has 16 different digits:
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
• Let’s convert 574 to hexadecimal:
• Continuously divide our number by 16, save the remainders
• Remainders give us hexadecimal BUT the Most Significant Digit (MSD) is bottom going up
• Also convert any number > 10 to a letter
• 14 = E
• Answer: 23E₁₆

MSD

LSD

Number Representation: Operations

• Let’s add two different bases: Find E4 + 101, then convert to base 8
• First convert both to decimal
• E4 → (15 * 16¹) + (4 * 16⁰) = 244
• 101 → (1 * 2²) +(0 * 2¹) + (1 * 2⁰) = 5
• Then add
• 244 + 5 = 249
• Then convert
• Answer: 371₈

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