Homework #1, Question #2

[William R. Lorenz]

I have a question about homework #1, question #2. In answering this,
pleae make sure you're not guilty of academic misconduct. :) I hope my
question is vague enough that answering this doesn't result in that.

Question #2 asks, "We understand what the number 101.101 (decimal)
represents. What value does 101.101 (binary) represent?" My question
for the group is: does the decimal in the binary number mean anything?
Could I just convert 101101 to decimal notation, or do I need to convert
101.101 to decimal notation? Is there any significance in the decimal?

Thanks, in advance, for any help you can offer.

[Mike Busch]

William,

There is plenty of significance in representing fractional parts of
numbers using binary. The decimal represents the place in the binary
where the 2^0 term is located (left of the .). This means that the place
to the right is 2^-1 and the second is 2^-2, and so on. So to answer
your question, you need to convert 101.101 and not 101101 to decimal.
There are strategies (ie doubling and halving) that simplify this process.

Please refer to the following link for instructions involving binary
conversion (about half way down is what you are looking for).
http://en.wikipedia.org/wiki/Binary_numeral_system
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+ +
+ Michael R. Busch +
+ UNIX Consultant/CSE Grader +
+ ***@cse.ohio-state.edu +
+ +
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Post by William R. Lorenz
I have a question about homework #1, question #2. In answering this,
pleae make sure you're not guilty of academic misconduct. :) I hope my
question is vague enough that answering this doesn't result in that.
Question #2 asks, "We understand what the number 101.101 (decimal)
represents. What value does 101.101 (binary) represent?" My question
for the group is: does the decimal in the binary number mean anything?
Could I just convert 101101 to decimal notation, or do I need to convert
101.101 to decimal notation? Is there any significance in the decimal?
Thanks, in advance, for any help you can offer.

[Wayne D. Heym]

My question for the group is: does the decimal in the binary number
mean anything? Could I just convert 101101 to decimal notation,

No.

or do I need to convert 101.101 to decimal notation? Is there any
significance in the decimal?

Yes, the binary point is significant.

Hint: 38.23 (as a decimal (base ten) representation) means:

3 x 10^(1) + 8 x 10^(0) + 2 x 10^(-1) + 3 x 10^(-2)