Wednesday, 20 July 2016

Binary Numbers

Binary Numbers:
Digital technology is all about 0 and 1.
How can you represent things using just 0 and 1?

8 - 10 year old students:
binary- unpack the language.
You have the choice of black or white + a dot!
Traditionally we have worked with the 10 base - using binary is using just 2.
The back - 1 = a bit. We can count to 1.
How can we build up the sequence?
Groups of 8 = a byte.
1, 2, 4, 8, 16, 32, 

On a CD there are about 6 million bits.

Challenge: (Maths, reasoning, problem solving, justify opinion, sequence)
Only using 5 cards to keep all the kids involved - larger groups and it is a management issue.

  • How can I have 11 dots visible? 1, 2, -, 8
  • Do you want the 16? Why is it out?
  • Do you want the 8? Why?
  • 21 dots = 1,-,4, -, 16
  • No, No, Yes, Yes, Yes - start at the highest end -, -, 4, 2, 1
  • Reason for the order - start with the most significant - the largest.
  • Least significant bit is on the right.
  • Most significant bit is on the left - focus on place value.
  • Conventions - we agree on these before, consistent.
  • Hexadecimal - chunking them in groups of 4 like place value.
  • Smallest number to represent? 1 (Wait, they will review - 0 - that make the All-Blacks!)
  • Can we count up in sequence 1, 2, 3, 4, 5, 6,  class help them... 7,  (one is very busy, every 2nd time - white for odd numbers.)
  • All other numbers are even. Add even numbers = even. No way they can make an odd number without the 'odd one'.
  • Even + odd = odd, Even + even = even.
  • Difficulty of number - 2 hardest, 4 next hardest as they have the most work to do.

  • 6 cards = 64 values
  • 5 cards = 32 values - adding one bit makes a huge different.
Security of bank account - 200 bits - how many combinations are there - huge numbers. It might take till the end of the world to hack your number. Secure because there are so many options.

201 bits - double the level of security.
  • How could I represent the letters of the alphabet? A - 1, B - 2, C - 4
  • Use sounds - conventions quack - white, Moo - black
  • Make Moo, quack, moo, moo, moo  rather than numbers- what letter of the alphabet? H or black, white, black, black, black
  • On a modem they were represented by high and low sounds. 

  • Can you represent all the letters of the alphabet?
  • Can we write a secret message?
  • What about macrons?
  • Can we agree on what number = macrons, ! , .  

  • Compose music:
  • Low, high, low, high - what's the letter? Low - 0, High - 1

  • Art:
  • Inverse koru - 0 or 1 - hiding messages in art - steganography
  • Can you make a secret message?

It is not about devices but our thinking skills...

Computational thinking:
Logic - right card is odd numbers
Algorithm - How to add 1
Decomposition - Break things into one section at a time
Patterns - doubling, all white is one less that next card, frequency of flips
Abstraction - ow to represent alphabet, numbers, texts, images
Evaluation - largest, smallest, How many bits needed to represent a given number

We start with a problem and look at how to solve them...
1. How to get a message out of a country with poor human rights record?
2. How to write a secret message?
3. How to represent Te Reo in the American system with no macrons?

Our privacy depends on our understanding of technology. (Need 2 locks)
Lock - encryption.
Put credit card details in a lock box. Pass through all the providers - all the kids.
How long should it take to get to America? Seed of light - a few seconds.
How can she unlock the encryption? phone, e-mail...... not safe.
She locks it in America with your encryption and send back to the start. I take my lock off, leaving just her lock on it. Send it back so she can access it.
It is secure all the journey and the sender or receiver don't need to share their secret codes.

This allows:
Secure secret voting system - know you voted but no record of who you voted for. (Some countries might be useful)
Codes on security depends on prime numbers!

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