bits and bytes

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Bits and Bytes: An 8th Grade Lesson:

Bits and Bytes: An 8 th Grade Lesson By: Rebecca Hersh

Lesson Objective:

Lesson Objective Students will be able to: Understand the fundamental principles of the binary system Convert between base ten and binary numbers Change letters into binary using ASCII

Lesson Materials:

Lesson Materials “Bits and Bytes” Presentation Computers with internet access Scrap paper for students

Lesson Outline:

Lesson Outline Introduction: The teacher will ask students how they think computers handle information like letters and numbers. This will prompt a brief introductory discussion. (5 minutes) The teacher will lead the “Bits and Bytes” presentation below. Students will complete the practice activities in the presentation (25 minutes) Students will practice converting binary numbers to base ten with an online game located at http://forums.cisco.com/CertCom/game/binary_game_page.htm (10 minutes) Closure: Students will convert the “OK” into binary on a piece of paper. This paper will be turned in as an exit ticket at the conclusion of class. (5 minutes)

References:

References Bradley, A. (2011). What is Binary?. About.com . Retrieved September 07, 2011, from http:// php.about.com/od/programingglossary/qt/binary.htm Harrell , S. (1999, November). Understanding Binary Code. Steveharrell.com/ . Retrieved September 07, 2011, from http:// www.steveharrell.com/computer/binary.htm McGuigan, B. (2003). What is Binary?. WiseGeek.com . Retrieved September 07, 2011, from http://www.wisegeek.com/what-is-binary.htm PC911 (2011). Bits vs. Bytes. PC 911 . Retrieved September 07, 2011, from http://pcnineoneone.com/howto/binary3 / Redshaw , K. (1996). ASCII Alphabet Characters . KerryR.net . Retrieved September 07, 2011, from http:// www.steveharrell.com/computer/binary.htm

Bits and Bytes:

Bits and Bytes An Introduction to Binary

What is Binary?:

What is Binary? Binary is also called “base two”. What base do you use in math class? In binary, only “0” and “1” are used. Each digit in a binary number is called a “bit”. Eight “bits” are called a “byte”.

Why Binary?:

Why Binary? Binary is used because computers run on transistors. A transistor is a switch that can be either “on” or “off”. When a transistor is “off”, a 0 is used. When a transistor is “on”, a 1 is used.

What About Place Value?:

What About Place Value? In base 10... In the number 13 , the 3 equals 3 . In the number 135 , the 3 equals 30 . In the number 312 , the 3 equals 300 . In the number 13,115 , what does the 3 equal?

What About Place Value?:

What About Place Value? In binary... In the number 0 1 , the 1 equals 1 . In the number 1 0 , the 1 equals 2 . In the number 1 0 0 , the 1 equals 4. In the number 1 0 0 0 , the 1 equals 8 . In the number 1 0 0 0 0 , what does the 1 equal?

What does each place equal?:

What does each place equal? 2 1 2 4 2,000 100 20 4 In the number 2,124 , each number has a different value. If we add each value, we get our number. 2,000 + 100 + 20 + 4 = 2,124

What does each place equal?:

What does each place equal? 1 1 1 1 1 16 8 4 2 1 In the number 1 1 1 1 1 , each 1 has a different value. Can you spot the pattern below? If we add it up, what does 1 1 1 1 1 equal? 16 + 8 + 4 + 2 + 1 = 31 1 1 1 1 1 = 31

Is there another way to understand it?:

Is there another way to understand it? For each number “1”, count what place value it is from right to left. Start with zero. 4 3 2 1 0 Next, calculate 2 to the power of the place value. In this case, it is 2 4 or 2 x 2 x 2 x 2 = 16 So, the number 1 0 0 0 0 equals 16

...and if that is too complicated?:

...and if that is too complicated? Then just remember the pattern! Can you sum up this pattern in one sentence? 1 1 1 1 1 16 8 4 2 1

What About Zeros? :

What About Zeros? When there is a 0 in the place value, you do not add that number. For example, the number 1 0 0 1 equals 9 8 + 0 + 0 + 1 = 9 1 0 0 1 8 0 0 1

Can we try some?:

Can we try some? Let’s practice with a chart first. 1 1 1 1 1 1 1 1 128 64 32 16 8 4 2 1 1 0 0 1 1 1 0 1 0 1 0 1

What are the answers?:

What are the answers? 1 1 1 1 1 1 1 1 128 64 32 16 8 4 2 1 1 0 0 1 9 1 1 0 6 1 0 1 0 1 21

Can we try some more?:

Can we try some more? Let’s try it without the chart. 1 1 0 1 1 1 1 1 0 0 0

What are the answers?:

What are the answers? 1 1 0 1 13 1 1 1 7 1 0 0 0 8

How does binary become letters?:

How does binary become letters? Every letter on your keyboard has a numerical value. This value is one “byte” long. How many digits (“bits”) will each letter have? To reach eight bits , every letter byte starts with “ 0 ”. The letter A is valued at 65 . What is 65 in binary? Answer: 0 1 0 0 0 0 0 1

Can you write in binary?:

Can you write in binary? Capital letters start at a value of 65 and go up from there. Here are some examples. A = 65 L = 76 Z = 90 Lowercase letters start at a value of 97 and go up from there.

Can you write in binary?:

Can you write in binary? Take the word Cat . C 67 01000011 a 97 01100001 T 116 01110100

Can you write “dog” in binary?:

Can you write “dog” in binary? Work with your group to write the four lowercase letters d o g in binary. d = 100 0 = 111 g = 103 Write your answer on your whiteboard. Leave space between each byte (letter). 1 1 1 1 1 1 1 1 128 64 32 16 8 4 2 1

Can you write “dog” in binary?:

Can you write “dog” in binary? The answer is.... 01100100 01101111 01100111

Can you write your initials?:

Can you write your initials? Choose the capital letter at the start of your first name. Remember that A = 65. What is your first initial’s value? Try to convert this number to binary. Ask a friend to check your work!

How to Practice?:

How to Practice? Try playing the Binary Game by Cisco! http://forums.cisco.com/CertCom/game/binary_game_page.htm