Converting Bits to Megabytes

Date: 02/11/2001 at 18:16:22
From: Brittany
Subject: Megabytes

This problem is confusing me: The human brain will store 100 trillion 
bits in its lifetime. 8 bits equal 1 byte, and 1,024 bytes equal 1 
kilobyte, and 1,024 kilobytes equal one megabyte. How many million 
megabytes can your brain store?

I don't know if I did this right, but would I do 1,024 * 1,000,000 ?

Date: 02/12/2001 at 12:55:51
From: Doctor Twe
Subject: Re: Megabytes

Hi Brittany - thanks for writing to Dr. Math.

I would do it as follows:

First, convert the number of bits to bytes by dividing by 8:

                                   1 byte   
     100,000,0000,0000,0000 bits * ------ = x bytes
                                   8 bits

(Notice that the 'bits' cancel, leaving the unit 'bytes' in the 
answer.)

Then take that answer and convert it to kilobytes by dividing by 1024:

               1 kilobyte
     x bytes * ---------- = y kilobytes
               1024 bytes

(Again, the 'bytes' cancel, leaving the unit 'kilobytes' in the 
answer.) 

Then take that answer and convert it to megabytes by dividing by 1024 
once again:

                       1 megabyte
     y kilobytes = * -------------- = z megabytes
                     1024 kilobytes

Once you find z, you have your answer. Incidentally, you can continue 
this beyond megabytes: 1024 megabytes = 1 gigabyte and 1024 gigabytes 
= 1 terabyte.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   Date: 02/12/2001 at 18:35:16

From: Brittany
Subject: Re: Megabytes

What I did is 1 trillion divided by 8, and I got 
12,500,000,000,000,000. Is that my answer? Sorry, but 
this is really confusing me!

Date: 02/13/2001 at 12:24:26
From: Doctor Twe
Subject: Re: Megabytes

Hi Brittany - thanks for writing back.

Assuming that the term 'trillion' was referencing the American system 
rather than the English system, you have three too many zeros after 
your number. For an explanation of the difference between the American 
and English systems for naming large numbers, see our FAQ on "Large 
Numbers and Infinity" at

  http://mathforum.org/dr.math/faq/faq.large.numbers.html   

100 trillion is 100,000,000,000,000 (14 zeros), so dividing by 8 gives 
12,500,000,000,000 (11 zeros) - 12.5 trillion bytes. So far, so good.

Now we have to convert those bytes into kilobytes and then megabytes. 
There are 1024 bytes in a kilobyte. Since kilobyte is the larger 
unit, we should have fewer of them. (Kind of like when changing 
pennies for dimes. Dimes is the larger unit, so we end up with fewer 
dimes than we had pennies, right?) So take our 12,500,000,000,000 
bytes and divide by 1024:

  12,500,000,000,000 bytes / 1024 = 12,207,031,250 kilobytes

How did I know that I should divide by 1024 instead of multiplying by 
1024? Because I needed a smaller number. Larger units, smaller number. 

Another way to do this is by "unit analysis" (or "unit cancellation"). 
This was the way I showed you yesterday. We set up a multiplication 
such that the units we want to get rid of (bytes in this case) cancel 
out, and the units we want to keep (kilobytes) don't cancel. The 
factor that we'll multiply by has to equal 1, so we have to make sure 
the top and bottom of the fraction are worth the same, just in 
different units. Using unit analysis, we multiply:

                              1 kilobyte
   12,500,000,000,000 bytes * ---------- = 12,207,031,250 kilobytes
                              1024 bytes

This way, the bytes in our starting number and the bytes in the 
conversion factor cancel, and the remaining unit is kilobytes.

Use whichever method you're comfortable with, and see if you can 
convert the 12,207,031,250 kilobytes into megabytes. (Remember that 
1024 kilobytes = 1 megabyte.)

I hope this helps. If you have any more questions or comments, write 
back again.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   

Date: 02/15/2001 at 23:53:10
From: Brittany
Subject: Re: Megabytes

I think I've got it. Would it be 11,920,929?

Date: 02/16/2001 at 13:28:55
From: Doctor Twe
Subject: Re: Megabytes

Exactly! (Well, not "exactly" - your answer is rounded off. The exact 
value is 296 kilobytes short of 11,920,929 megabytes. But that's the 
correct answer rounded to the nearest megabyte.) Well done!

If you have any more questions or comments, write back again.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   

Date: 02/16/2001 at 22:04:26
From: Brittany
Subject: Re: Megabytes

Thanks for helping me!