Cynthia Lanius

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Power Cards

Application - Binary Numbers
Power Cards Intro || The Trick Explained || Blank Cards || Application - Binary Nos.
More of Cynthia Lanius' Math Lessons

Let's use this mathe-magic trick to demonstrate a nifty way to write numbers as binary or in Base 2. Read this excellent description from the Math Forum of how computers or calculators use binary numbers.

We ordinarily write numbers in base 10. That means there are 10 digits, 0-9. For example, consider 209 in ordinary base 10. You know that is 2 hundreds, plus 0 tens, plus 9 ones. Hundred, ten, and one are all powers of 10, our base. So we could think of it this way.

Base 10
100101
102101100
209

 
Note: If you need an explanation of 0 as an exponent, here's a good one from the Math Forum.

Now we can easily use this same method to write numbers in base 2. Instead of powers of 10, we use powers of 2, and remember we can only use 2 digits -- 0 and 1. Let's convert 28 in base 10 to base 2. Remember from our Power Cards that 28 = 16 + 8 + 4.

Base 2
168421
2423222120
11100

So 28 in Base 10 = 11100 in Base 2.

Now see how the Power Cards relate to binary numbers? See the chart below. If the number is in the card, it gets a 1 in that slot; if not, it gets a 0.

Base 2
Card 5Card 4Card 3Card 2Card 1
168421
2423222120
11100

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Card No. 2
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Card No. 3
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Card No. 4
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Card No. 5
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Power Cards Intro || Print Version || The Trick Explained || Blank Cards || Application - Binary Nos.
More of Cynthia Lanius' Math Lessons
URL http://math.rice.edu/~lanius/pro/power4.html