SOLUTION: My problem involves the base ten numeration system. I need to write 101(0two) (zero and two written like an exponent)in base ten.

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Question 202161: My problem involves the base ten numeration system.
I need to write 101(0two) (zero and two written like an exponent)in base ten.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not clear on your question. I think you are asking
What is 101%5B2%5D in base 10?
If that is the case, then you need to understand that the each column in the binary system has a specific value. Just like each column in base ten has a value.
In base ten, the lowest order column (digits) represents 10%5E0 = 1
The next higher column represents 10%5E1 = "the tens"
The next one up is 10%5E2 = "the hundreds".
Same idea in other base systems.
For binary (base 2),
the lowest order column (digits) represents 2%5E0 = 1
The next higher column represents 2%5E1 = "the twos"
The next one up is 4%5E2 = "the fours" etc
So the number you are given is 101%5B2%5D
Thus you have 1 in the digits. so that is 1*1 = 1
You have 0 in the twos. 2*0 = 0
You have 1 in the fours. 4*1 = 4
Total is 4+0+1 = 5
So 101%5B2%5D = 5%5B10%5D
The same process holds for any base you choose. Popular bases include 2, 8, 10 and 16 as far as computers are concerned. can you think of a case where base 12 occurs in real life?
Take your "time" and think about it