# Math Help - Binary Digit & Decimal value

1. ## Binary Digit & Decimal value

can someone check if I did this correctly

the human genome contains about 3 billion base pairs...stored in a computer as a sequence of $3*10^9$ bases X 2 bases/bits = $6*10^9 bits$
The Encyclopedia Britannica has about 1500 words per page, 1000 pages per volume and 30 volumes. How many sets of the Encyclopedia Britannica would it take to store the same amount of info in a single strand of human dna?
$
1500*1000 = 1,500,000 = 15*10^5$

$(15*10^5)*30 = 45,000,000 = 45*10^6$

$(45*10^6)base * 2(bits/base) = 9*10^7 bits$

$\frac{(6*10^9 bits)}{9*10^6} = 66.67$

2. I see two problems

How are you doing this calculation without knowing the number of letters on each page, since a word contains more than one letter, and thus can hold more than one bit of information.

Next, what does this calculation mean?

I see (number of words in 30 volumes)*2 bits/base

but... I thought "base" referred to a "base pair" of dna. Why are you multiplying the number of words by 2 bits?

there are 26 letters in the alphabet, 10 decimal digits in the base 10 number system and several different kinds of punctuation marks, two possibilities for capitalization (on/off) and a few other symbols used in a typical book. A combination of 6 binary bits can take on 64 different possibilities which is about the number needed to create a code equivalent to all the possible characters that make up normal text. the average word in a text contains about 5 characters and with each character requiring 6 bits for its representation, 1 average word of text is equivalent to about 30 bits

4. the human genome contains about 3 billion base pairs...stored in a computer as a sequence of bases X 2 bases/bits =
I believe you mean 2 bits / bases. This is because there are four possible values at each base pair, and 2 bits holds four values, as desired.

The Encyclopedia Britannica has about 1500 words per page, 1000 pages per volume and 30 volumes. How many sets of the Encyclopedia Britannica would it take to store the same amount of info in a single strand of human dna?
Let b be the number of bits in a strand of the human genome. What you want is

$b / (bits per word) / (words per page) / (pages per volume)$

this 'convert's bits to volumes. If you want sets of 30 volumes, then just divide this by 30.

5. so it would be (6*10^9) / (30) / (1500) / (1000) = 133.333

133.33 / 30 = 4.4

6. That is what I have, as long as I am understanding the problem correctly that should be correct.