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| Math Central | Quandaries & Queries |
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Question from Jan, a parent: I need to know how to figure this one out. A computer word is made of strings of 0's and 1's. How many different words can be formed using 8 characters? Thanks |
Hi Jan,
How many different words can be formed using 1 character?
The answer is 2, they are 0 and 1.
How many different words can be formed using 2 characters?
Each of the two, one character words can be made into two, two character words by appending either a 0 or a 1 to the end. Thus there are 2 × 2 = 22 = 4 two character words.
How many different words can be formed using 3 characters?
Each of the four two character words can be made into two, three character word by appending either a 0 or a 1 to the end. Thus there are 4 × 2= 23 = 8 three character words.
How many different words can be formed using 4 characters?
Each of the eight three character words can be made into two, four character word by appending either a 0 or a 1 to the end. Thus there are 8 × 2= 24 = 16 three character words.
Can you complete the problem now?
Penny
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