Binary numbers are the basis for how computers work. They consist of only two digits, 0 and 1, whereas the standard number system is base 10 with ten digits. Computers use the binary system because their internal workings are based on two states - on or off, which can be represented by 1 and 0. The document teaches students about place value in binary, has them practice converting numbers between binary and base 10, and explains that understanding binary is important because it shows how computer processing works digitally with two states.

1. Binary Numbers
MS. LAUREN GAUTIERI

2. OBJECTIVE:
SWBAT understand the purpose of binary numbers.
SWBAT understand the relationship between binary numbers and computing.
SWBAT convert numbers from the standard number system to the binary number
system.
Audience
Middle School Grades 6-8
Teaching Method(s)
Teacher-directed interactive power point (Visual/Audio)
Cooperative learning practice
Individual practice
Student Activities
Note-taking
Group work
Individual practice
Assessment
Homework
Accommodations/Modifications
Power point made accessible online for students
Enrichment activities

3. What are binary numbers?
 Have you ever turned on your computer and noticed a
bunch of numbers run across the screen?
 If you looked closely you would have noticed that
although it looked like a ton of numbers, there were only
actually two different digits present.
 These two digits are known as binary numbers.
 Binary is a special number system that consists of only
two numbers. Those numbers are 0 and 1.

4. Wait! What? I don’t
understand…
LET’S THINK ABOUT THIS…
THE BINARY SYSTEM HAS TWO DIGITS
0 AND 1
THE STANDARD NUMBER SYSTEM WE KNOW HAS HOW
MANY DIGITS? TEN DIGITS
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
SO, NOW I KNOW THAT THE BINARY SYSTEM IS MADE
UP OF 2 DIGITS WHILE THE STANDARD NUMBER
SYSTEM IS MADE UP OF 10.

5.  The number of digits in a number system is referred
to as the BASE.
 Therefore the standard number system contains 10
digits so it is considered to be Base 10.
 If the binary number system contains 2 digits, then it
would be considered…Base 2.

6. Understanding Base 10
Take a look at the video below to help you better understand what
Base 10 really means… (Click below)

7. Refresh your memory and try it with a partner…
629
452
 The 4 is in the hundreds
place.  Now it’s your turn…
This means you have
4 x 100 or 400
 The 5 is in the tens place.
This means you have 5 x
10 or 50.
 The 2 is in the ones place.
This means you have 2 x 1
or 2.
 Together, 400 + 50 + 2
= 452

8. Okay cool…I get it now. But
what’s the point?
BINARY NUMBERS ARE THE BASIS FOR HOW COMPUTERS WORK.
COMPUTERS ARE PROGRAMMED WITH THE BINARY NUMBER SYSTEM
BECAUSE COMPUTERS ARE DIGITAL AND HAVE TWO STATES.
COMPUTERS ARE EITHER ON OR OFF.
THE "ON" STATE IS REPRESENTED BY THE NUMBER "1", WHILE THE "OFF"
STATE IS REPRESENTED BY THE NUMBER "0".

9. Understanding Base 2
 From the video earlier we learned that Base 10 goes
up by multiples of 10. Now we are going to switch
gears and talk about Base 2. This means that the
place value goes up by multiples of 2.
128 64 32 16 8 4 2 1
 Simple so far…right?

10. Understanding Base 2
 Now let’s apply everything we know about place
value in base 10 to Base 2. (Click below to see how it
works)

11. Watch how it works…

12. Let’s try some together

13. Now you try it with your partner…
Convert 78 to base 2: Convert 100101 to base 10:

14. Exit Ticket
IN YOUR OWN WORDS EXPLAIN TO ME THE
PURPOSE OF BINARY NUMBERS.
WHAT IS THE POINT OF CONVERTING NUMBERS TO THE
BINARY SYSTEM?
WHAT ARE BINARY NUMBERS USED FOR?

15. HOMEWORK
CONVERT THE FOLLOWING NUMBERS FROM BASE 10 TO
BASE 2
46
32
87
CONVERT THE FOLLOWING NUMBERS FROM BASE 2 TO
BASE 10
110101
001101
111001

16. Enrichment: Challenge yourself…
We learned about number systems and bases. What if I wanted to convert
the number 82 (base 10) to base 5?
Use what you learned today about the basic principles of place value to
see if you can figure out what the number 82 would be if you were to
convert it to base 5?

17. Information gathered from the following resources:
www.swansontec.com/binary.html
www.basic-mathematics.com/binary-number-system.html
Video Resources:
Showme.com – self created interactive whiteboard lessons
http://vimeo.com/groups/132679/videos/19721329