# Thread: base 10 and base 2

1. ## base 10 and base 2

I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.

2. Originally Posted by homeschoolrocks
I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.
No one can help you if you do not post a particular problem or question.

3. Originally Posted by homeschoolrocks
I am having trouble with 8th grade math - prealgebra in base 10 and base 2. Can someone please explain it to me? Instead of the exponent being in the upper corner it is in the bottom corner. I don't understand it at all. Thank you.
Do you mean something like

$24_{10} = 11000_2$

If so:

A decimal number is the sum of products of a one digit number (vulgo cipher) and a power of 10 which indicates the place of the cipher in the number. (The ciphers start always at zero and the maximum cipher is 1 smaller than the base) That means:

$24_{10} = 2 \cdot 10^1 + 4 \cdot 10^0$

In a similar way a number base 2 is constructed. There are only 2 ciphers (0 and 1; see remark above). Therefore

$11000_{2} = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 +0 \cdot 2^1 +0 \cdot 2^0$

which yields 24 as a decimal number.

4. ## Thanks

Thanks for the help everybody! I am going to use this message board in the future.