base 10 and base 2

[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.

 

[pka]

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.

 

[pappus]

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

\(\displaystyle 24_{10} = 11000_2\)

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:

\(\displaystyle 24_{10} = 2 \cdot 10^1 + 4 \cdot 10^0\)

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

\(\displaystyle 11000_{2} = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 +0 \cdot 2^1 +0 \cdot 2^0\)

which yields 24 as a decimal number.

 

[homeschoolrocks]

Thanks

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