Binary Number System Activities for Middle School Math
The binary numeral system refers to the representation of values using only two symbols, 1 and 0. Because of its straightforward usage in circuits, the binary system has been established as the language of computers. Binary numbers are based on the exact principals of the decimal system (the 0 to 9 system) and particularly on place values and exponentiation; hence, activities on binary numbers will help middle school students practice on both topics.
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Count Dots
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In the binary system, what would otherwise be the ones place value is actually the equivalent of (1 --- 2^0), the tens values is (1 --- 2^1) and so on. Numbers are formed when you multiply those values by 1 or 0 (which results in 0) and then adding them together. You can depict the exponentiation with dots on a set of cards. The first card, starting from the right, will be the ones card and have one dot. The second card -- the tens card -- will have two dots, the third will have six dots and so forth, until you have made five or six cards at the most. Give a number using the binary system, for example 11001, and let children find its decimal equivalent. Kids must count the dots of the ones, thousands and tens of thousands cards, disregarding the second and third cards.
Form Birthdays with Binary Numbers
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Students must write down their date of birth, using the binary system. Under the supervision of the teacher, students must utilize exponentiation to transform their decimal birthday, such as 02/17/98, onto binary numbers. For this example, the kid must do 0 --- (1 --- 2^0) + 1 --- (1 --- 2^1) = 0 + 2 = 2. The day and year will be somewhat more difficult to find out; that's why the dot cards from the previous activity can be helpful for students who seem to fall behind.
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Video Games Consoles
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From the age of the old Atari 2600, up to the PlayStation 2 era, every generation of games consoles was defined by their processors' capacity. Thus, there were the 4-bit consoles, like Atari 2600, 8-bit (NES), 16-bit (Sega Mega Drive), 32-bit (PlayStation), 64-bit (Nintendo 64) and 128-bit (PlayStation 2). You can download a picture of each of these consoles and place them in the board, from right to left. Write a number under each picture and ask students to find the decimal equivalent. The first two places, which are not represented by any console, must always take the 0 value.
Code and Decode Messages
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This activity resembles the broken telephone game, where each kid has to whisper a message to the next, but this time this will be done with notes. Give each student a number, which he or she has to add to -- or subtract from -- the number the previous kid passes on. Note down the number you gave each kid to evaluate the final result. Give the number 1 to the first student and ask him to transform it from binary to decimal (it's the same on this occasion), add the number you had given beforehand, transform it back to binary and pass it to the next student. Make sure the numbers are not exceptionally high, to move the game relatively fast.
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References
- Photo Credit Jupiterimages/Photos.com/Getty Images
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Comments
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Tasos, there were no 4-bit consoles. The Atari 2600 is 8-bit, it uses the 8-bit 6507 microprocessor and an 8-bit data base. The confusion arises that bitness was purely a marketing term, and even then one that actually did not start until the time of the Sega Genesis' release in '89. Bitness of the console has little to do with the console's graphics capabilities, rather that is defined by the actual graphics support chips. Hence you have the Atari 2600 and NES, two 8-bit consoles with vastly different graphics capabilities. Or likewise the Intellivision (which is 16-bit) vs. the Genesis.
