Presentation 9: Binary system

Resources
paper and pencil for every child

Presentation

Bulbs

How does a computer store numbers?

Get some answers.

Let me tell you a story. A few years ago, maybe 30-40 years ago, computers were HUGE. Like a whole building. And they stored numbers with bulbs - on or off
Draw two bulbs, on and off.

People figured: they can use off state to store 0, and on state to store 1. But then they saw a problem? How do they store 2, 3, 4?

Have kids suggest solutions.

One bulb is not enough to store more than 0 or 1, so people decided to add another bulb. Now they could store...

(draw bulbs on and off instead of 0 and 1, used in this document)

00 - 0
01 - 1
10 - 2
11 - 3


Combinatorics
You see, 2 bulbs is enough to store 4 different digits - 0,1,2,3.
Let's see how many different numbers you can store with 3 bulbs!
Let me start

0 0 0 - all off
0 0 1 - off ,off, on
...
Please continue to add to this list all possible states of 3 bulbs and let me know how many you got!
Let's see who gets the most number of combinations!

Make sure kids have something to write on

Encourage kids to look for more combinations. Show more examples to those who don't understand. Find duplicates for those who find more than 8.

Ok, let's do it together now!

0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0 
1 1 1

(It wasn't obvious to me how I explain the way I go about ordering the combinations, without kids getting exposure to carry-ons yet)

So, how many numbers we can represent? Let's see:

000 - 0
001 - 1
010 - 2
011 - 3
100 - 4
101 - 5
110 - 6
111 - 7

Encoding and decoding

Now, imagine we want to write number 341, how would we represent it with bulbs?

(This works only is 341 - octal representation of a number, not a decimal)

3 - 011
4 - 100
1 - 001

So we get 011 100 001

Exercise: Write in binary the following number : 562

Have kids  try first and then show the correct result - 101 110 010

Now, let's try to figure out what number is represented by the following binary:

001 100 011 110
 1     4     3    6

1,436!

Exercise: What number is represented with the following binary: 101 111 100 010?
(5,742)

Beyond 7
As you can see 3 bulbs can represent digits from 0 to 7. What about 8? Who can figure out how to represent 8?

(In my class about 5 kids volunteered - all of them tried to come up with a "missing" sequence of 3 bulbs, every time i had to point them to the duplicate - a digit that's already represented by a suggested sequence. Finally somebody proposed 4th bulb)

You can't represent 8 with 3 bulbs - there are not enough combinations of bulbs for it. So you need the 4th bulb!

If you have time left, have kids use 0 and 1 instead of drawing bulbs, go into combinations of 4, see other patterns, such as: 10 - 2, 100 - 4, 1000 - 8, 10000 - ?

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