MS. LAUREN GAUTIERI

Binary Numbers

AudienceMiddle School Grades 6-8

Teaching Method(s)Teacher-directed interactive power point (Visual/Audio)Cooperative learning practiceIndividual practice

Student ActivitiesNote-takingGroup workIndividual practice

AssessmentHomework

Accommodations/ModificationsPower point made accessible online for studentsEnrichment activities

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.

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.

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.

Wait! What? I don’t understand…

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.

Understanding Base 10

Take a look at the video below to help you better understand what Base 10 really means… (Click below or visit video on youtube)

452452 629629The 4 is in the hundreds

place. This means you have 4 x 100 or 400The 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

Now it’s your turn…

Refresh your memory and try it with a partner…

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".

Okay cool…I get it now. But what’s the point?

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.

Simple so far…right?

128 64 32 16 8 4 2 1

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 or visit my youtube link.)

Watch how it works…View on youtube

Let’s try some togetherYouTube link

Convert 78 to base 2:Convert 78 to base 2: Convert 100101 to base 10:Convert 100101 to base 10:

Now you try it with your partner…

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?

Exit Ticket

CONVERT THE FOLLOWING NUMBERS FROM BASE 10 TO BASE 2

463287

CONVERT THE FOLLOWING NUMBERS FROM BASE 2 TO BASE 10

110101001101111001

HOMEWORK

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?

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 lessonshttp://vimeo.com/groups/132679/videos/19721329