Binary Numbers Notes To The Volunteer


Binary Numbers Notes to the Volunteer
Arithmetic in bases other than ten is often used as an enrichment activity to deepen
understanding of base ten and of place value systems in general. Binary numbers not only serve
as an example of a place value system in another base but also are the fundamental number
system of the computer. Several activities are associated with this module:
1. The magic card trick.
2. Binary weights: weighing objects of different mass to change base ten to binary.
3. Addition on the binary adding board.
Counting and adding in binary.
If you have two or more children at this activity, you may want to encourage some friendly
competition with the adding board.
In binary, 1 + 1 = 10. That means, whenever you add 1 in any place to 1 in the corresponding
place you need to carry a 1. Answers to problems in binary:
Count in binary from 10000 to 100000: 10000, 10001, 10010, 10011, 10100, 10101, 10110,
10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000.
Binary addition problems:
111+110 = 1101
1101+1110 = 11011
111011 + 11 = 111110
1101101 + 110011 = 10100000
111101 + 10101 = 1010010
The Magic Card Trick
Materials needed: a printout of each of the five magic cards.
This trick piques the curiosity of kids, who in turn love to try it on others.
It shows up in the Mathematics for Elementary Education course taught at Iowa State, and I have
seen it in the Highlights Mathmania children's puzzle books.
You will need to offer to play a trick on the visitors to your display. To play the trick,
ask your "victim" to think of a number between 1 and 31. Then you ask your "victim" which
cards contain his/her number. Then rapidly produce an answer, leaving your "victim"
wondering how you could possibly read his/her mind. The secret is that you add up the numbers
on the top left corner of each card the "victim" identifies. The numbers on card A are all the
numbers with a binary representation having a 1 in the ones place. The numbers on card B are
all those with a binary representation having a 1 in the twos place. Card C: a 1 in the fours
place. Card D: a 1 in the eights place. Card E: a 1 in the sixteens place. The trick is a great
lead-in to explaining the binary system--once you've played it on your "victim" once or twice he
or she will want to know how it works. The explanation in a nutshell: any decimal number can


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