# NCAA, Binary Trees & More

This is an outline to a lesson I did for my 5th grader’s math class during the NCAA tourney

#### Ask class to write down the answers to the following “Opening Questions”

Assume all teams have a 50% chance of winning any game

How many games must a team win to get to the Final Four?
4
What’s the chance a team make it to the Final Four?
1/16
What’s the chance a team has to win the tournament?
1/64

#### Base-10 number system review

How many digits do you need to represent 29,851?
5

#### Base-2 number system explanation

Give example of how to represent 9
1001

How many digits do you need to represent 25? Represent it
5 —> 11001
Display the numbers 1 through 8 in binary
0: 0
1: 1
2: 10
3: 11
4: 100
5: 101
6: 110
7: 111
8: 1000

#### Binary in real life

• Computers use binary or base-2 number system because electricity is either on or off
• A letter like “X” in computer language is represented by ASCII 120. In binary that is 1111000
• A pixel on your computer screen can be any of a million colors.
• Color Name: (Decimal RGB), (Binary RGB), (Hexadecimal RGB)
Blue: (0,0,255), (00000000,00000000,11111111), (00,00,FF)
Cyan: (0,255,255), (00000000,11111111,11111111), (00,FF,FF)
Hexadecimal is base-16 so there’s a ones place, a 16th place, a 32nd place and so on.
• 16 characters are 0-9, A-F
• A byte is 8 bits
• megabyte is 1mm bytes…how many bits? (8mm)
• gigabyte is 1000 megabytes
• terabyte is 1000 gigabytes
• How many songs can a 1 gigabyte hard drive hold? (200)
• How about a 1 TB hard drive? (200,000)

4K movie is about 20 GB
• Every frame has 3840 pixels horizontally and 2160 pixels vertically —> about 8.2mm pixels!
• Each pixel is a color that requires several digits or bits to represent it (perhaps 1 byte per pixel)
• So there are about 8 MB per frame!
• Standard movie is 24 frames per second so need 192 MB/s
• Movies is 90 x 60s = 5400 seconds
• 192 MBs x 5400 seconds = 1mm MBs = 1 terabyte!
• Compression of 50 to 1 gets the movie down to 20 GB

#### Fun Stuff

How high can you count if you use your fingers to represent numbers using binary notation?
1023
How many fingers do you need to represent each letter of the alphabet?
5 using number to letter cipher

For Zak’s Class