Binary Numbers Notes To The Volunteer printable pdf download

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

11011+1100=10011

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

Binary Numbers Notes To The Volunteer