akohl
  • akohl
Jane is considering a new TV She has an existing 50Mb/s connection through her Internet provider A 1080p HD movie typically requires about 5GB/hour storage space How long will it take her to download a 90 minute movie in 1080p resolution
Computer Science
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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rsmith6559
  • rsmith6559
About 21 minutes.
mathmate
  • mathmate
Network speed is usually expressed in megabits/second, mbps, or Mb/s. For communications, megabit is 1,000,000 bits. For storage, Gb=2^30=1,073,741,824 bytes (except that disk manufacturers use 10^9 bytes as 1 Gb) One byte = 8 bits. So 45 minutes at 5Gb/hour would transfer 5*(2^30)*(45/60) bytes = 4,026,531,840 bytes The claimed download speed of 50 mbps is 50*(1,000,000)/8 = 6,250,000 bytes/s Time required according to claimed download speed =4026531840/6250000 seconds = 644.2 seconds = 10.7 minutes. HOWEVER, actual download speeds are much lower, depending on the number of users, interference, quality of transmission, etc, and rarely achieve 25-50% of the claimed speed.
e.mccormick
  • e.mccormick
mathmate, you are using 1,000,000 for meg, when it is really 1,048,576. But simpler math is to realixe that the difference between gig and meg is a multiple of 1024, so: 5GB * 8 bits * 1024 * 90/60 minutes/hr = total mega bits. Then they can just divide out the 50 and get it in seconds.

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mathmate
  • mathmate
@e.mccormick I thought so too, at the beginning, but the following is what seems to be the case after reviewing a few sources. MB in computers is an extension of KB which means (most of the time) 1024 bytes. However, I came to understand that in data communications, megabit has been traditionally used to mean (literally) \(10^6\) bits. And worse, disk manufacture follow suit, so a 500 GB disk gives us only \(500*10^9\) bytes only, although in other contexts such as file storage, MB still means \(2^{20}\) bytes in most cases. At the time when disks were sold as 20 or 30 MB (my first), it didn't make much difference. Now for a terabyte disk, the difference is substantial at 9%! In any case, 2.4% does not make a big difference to someone downloading a video. It takes what it takes, lol. And simpler math is probably preferred.
e.mccormick
  • e.mccormick
The computer companies play games with disk size. They used to measure them in \(2^x\) type balues, but then some enterprising person figgured out the numbers were larger if they used base 10 rather than base 2. This is why unformatted disk size is given in base 10 and related to why they seem to fill up fast. File systems use base 2. This is why file systems look smaller than the marketed size on a disk. This gives the illusion that the disk is filling up faster or that the disk is smaller, but it is just getting the true size. In data communications, they use actual bits and measure everything by the bit. So transfer rates are always given in base 2. For a file size and a transfer rate, you get actual base 2 numbers, so \(K = 2^10), \(M = 2^20), \(G = 2^30), and so on. How much a difference it makes depends on the accuracy of the answers. In a data communications class you can easily run into questions where they intentionally make the margin of error such that using base 10 will result in getting it wrong. The goal of this is to force people into using binary, which is really not mathematically hard. And it is still smaller numbers and simpler to use *1024 rather than expanding it completely in base 10 to 1,000,000.
mathmate
  • mathmate
It turns out that, in data communications especially, when we measure in bits, the words giga, mega, kilo take on their literal meaning based on base 10, i.e. 10^9, 10^6 and 10^3. I have not found out the historical reasons why this was done in data communications, but I believe it could have something to do with simpler measuring instruments' unit conversions. Numerous sources explain the phenomenon, but not historically why. Examples: http://www.lyberty.com/encyc/articles/kb_kilobytes.html http://www.checkyourmath.com/convert/data_rates/per_second/megabits_kilobytes_per_second.php
e.mccormick
  • e.mccormick
Note the upper and lower case on what you linked: http://www.lyberty.com/encyc/articles/kb_kilobytes.html K = 1024 k = 1000 M = 1024^2 m = 1000^2 g = 1024^3 G = 1000^3 The question uses upper case, not lower. Also, while Ethernet uses base 10 and a lower case letter, we are not discussing Ethernet. Internet providers traditionally base off of T1 lines, which are 24, 8 bit channels. Each channel does 8kHz making it 64kbit, which is the base that is used. Because 64kbit channels work nicely with base 2 math, they use base 2 in most internet circuits. Now, there is a slow transition to Ethernet in some segments of telecommunications, so it is not strictly the rule that you use base 2 at all times, but you will see a lot of things that are multiples of 64 thanks to them being bundles of the previous speed set. So a DS3 is 28 DS1 lines or 28*24=672 DS0 channels. As before, each channel is 64kbits. It goes on and on like this, so there is some really odd math, but in use of base 2 helps you split it up in lilttle friendly blocks. fyi: I work for an internet service provider and have dealt with this issue for a long time.
mathmate
  • mathmate
I guess can't argue with an expert in the field. By the way, inferring from what you said, I gather there is a typo between G and g.
ParthKohli
  • ParthKohli
m is not \(1000^2\) -- it stands for milli, an SI prefix which stands for \(10^{-3}\). Like for example, it's used in millilitres. A millilitre is one-thousandth of a litre. What that means is that if I take 1000 millilitres, I will get a litre. That's what I basically mean by \(10^{-3}\). A millilitre is indicated by \(ml\), so m is actually reserved for milli. You can attach milli to other SI units too! I have a millimetre for length (That means if I take 1000 millimetres, I will get the same as 1 metre right?) Hope you got it now :)

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