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!
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