Part of Unit: Operating Systems
Lesson Plan Overview / Details
Computers think only in binary, using only ones and zeroes. However, just a one or zero, called a "bit", will not give enough information for a computer to do anything useful with. We string together 8 bits to get a binary number that will give us 256 possible numbers, enough to do something useful with.
- 150 Minutes
California Career and Technical Education Standards
Objectives and Goals
- Students will be able to understand how decimal numbers can be represented in binary with only bits of ones and zeroes.
- Students will understand the concept of a "byte" and how it is important to the computer industry.
- Students will be able to convert decimal numbers into binary.
- Students will be able to convert binary numbers into decimal.
- Students will understand why a byte of information cannot have a value over 255.
Activities in this Lesson
- Opening Activity - Hooks / Set
Show the attached video, "A Single Grain of Rice". It tellsthe fictional story of the invention of the game of chess. In this story, the inventor is granted any request by the Emperor he works for. He asks only for this: a grain of rice on the first square of his chessboard, to be followed the next day by two grains on the next square, then four on the next and so forth doubling the amount each day until the board is filled. The Emperor is glad to grant his request, but soon realizes that there is not enough rice in the entire world to fulfill it!
Ask the students "Which would you rather have, two million dollars right now, or a penny doubled every day for a month? (30 days)" Give them some time to work out the math and then have them compare answers and how they arrived at their solutions. You can find a solution here.
Now point out to them that this is how computers can make large numbers out of simple bits that only have two values. As they create binary numbers by linking bits together, each bit doubles the possible value of the total number. Computers put 8 bits together to make a byte, which has 256 possible values.
- Alternate Opening Activity - Hooks / Set
Play the Powerpoint Powersof2.ppt. Ask the students what theme they see in the numbers. Point out the progession 2-4-8-16-32-64-128-256-512-1024. Write these numbers on the board and ask the students what type of progression they see.
The students should say that the numbers represent powers of 2. If not, explain it to them.
- Powers of 2.ppt [ Download ] Powers of 2.ppt
- Lecture - Lecture
Computers think in terms of bytes. A byte is 8 bits strung together to make one long number. A bit has two possible values, “1” and “0” which is why almost all computer values come in powers of 2. This is where the string of numbers in the powerpoint come from- 2=2 1, 4=2 2, 8=2 3, 16=2 4, 32=2 5, 64=2 6, 128=2 7, 256=2 8, 512=2 9 and 1024= 2 10.
Compare this to the decimal number system where the places in a decimal number are powers of 10-
10 0=1, 10 1=10, 10 2=100, 10 3=1000, etc.
Note that the first value in a binary byte is the ones place, which is 2 0.
- Demonstration - Demo / Modeling
Use the attached powerpoint, Binary Decimal Conversion.ppt to illustrate how the number 176 would be represented as a binary byte.
Show the students how to convert a binary byte back to a decimal number by reversing the process.
1011000 = 1x128 + 0x64 + 1x32 + 1x16 + 0x8 + 0x4 + 0x2 +0x1 = 128+32+16=176.
Encourage the students when doing binary to decimal conversion to begin by writing the number chart above the binary digits-
128 64 32 16 8 4 2 1
This will make the conversion easier.
- Binary Decimal Conversion.ppt [ Download ] null
- Practice - Guided Practice
Write the number 213 on the board. Have the students take a piece of paper and title it Binary Byte Lab. Have them write their name on it in the upper right corner.
Have the students convert the number 213 into a binary byte using the method you just demonstrated and write the process they used on the paper. When they are done, have them compare their result with the student next to them.
They should get binary 11010101.
- Lab Activity - Independent Practice
Lower down on the paper, have them make two columns and label them “Decimal” and “Binary”. Under the binary heading, have them write the numbers 128 64 32 16 8 4 2 1 as a reminder to help them.
In the “Decimal” column, have them write these decimal numbers: 231, 127, 196, and 20. Have them convert the numbers to binary and write the results in the “Binary” column.
Now have them move down the page and write these numbers in the “Binary” column: 11011100, 00101101, 10111001, and 00010110. Have them convert these numbers to decimal and write the answers in the “Decimal” column.
- Closing Activity - Closure
Move around the room and check their work. After you are satisfied with their work, have them open a calculator on their computer. Their calculator should have a scientific setting (in Windows it is under the “View” tab.) There should be a setting in the calculator that allows numbers to be translated between decimal and binary. Have them check their work using the computer calculator.
- Assessment Quiz - Assessment
Print out the attached quiz. Have the students do it WITHOUT the help of calculators.
- Decimal- Binary Conversion Quiz [ Download ] null
- Enrichment - Other
In some movies, you will see a computer specialist or hacker type an IP address, which should consist of 4 numbers separated by dots (periods). They will look like this: 220.127.116.11. To the computer, an IP address is actually 4 binary bytes. If you look closely at these numbers in the movies, we will notice that one of the numbers is always over 255. Why is that?
(Hint: Why do telephone numbers in movies always start with 555?)
- Assessment Types:
- Demonstrations, Teacher-Made Test, Observations,
Teacher will assess by checking the lab write-up and the quiz. Teacher can also assess based on observation during the guided demonstration and lab activity.