Binary Numbers Magic Trick
Binary Numbers Magic Trick
Math Circle April 07 2013
Can you read people's mind?
Pick a number from 1 to 63 If your number appear in the card say yes,
otherwise say no
Let's guess which number you picked
What is the trick?
Let's start with a simpler case: Pick a number from 1 to 3
2
1
3
3
Can you guess the trick?
A little more complicated case
Pick a number from 1 to 7
4
2
1
5
3
3
6
6
5
7
7
7
Suppose you can only use 0 and 1 as your digits
Suppose you can only use 0 and 1 in your number system. Can you express every number in terms of 0 and 1 only?
Our ordinary numbers are called " base-10 number system" or "decimal" because.... 798 = (7 x 100) + (9 x 10) + (8 x 1) = (7 x 10 x 10) + (9 x 10) + (8 x 1) = (7 x 102) + (9 x 101) + (8 x 100) Note that 100 = 1, (any non-zero number)0 =1
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