Question #8033

Suppose the size of an uncompressed text file is 1 megabyte. How long does it take to download the file over a 32 Kilobit per second modem? How long does it take to take to download the file over a 1 megabit per second modem? Suppose data compression (6 times) is applied to the text file. How much do the transmission times change?

Expert's answer

Size: 1 megabyte = 1 048 576 bit

Rate: 32 Kilobit/s = 32000 bit/s

Time: T = 1 048 576 bit / 32000 bit/s = 32.768 s.

Rate: 1 megabit/s = 100 000 bit/s

Time: T = 1 048 576 bit / 100 000 bit/s = 1.048576 s.

After compression:

Size: 1 048 576 bit / 6 = 174762.(6) bit = 174763 bit

Rate: 32000 bit/s

Time: T = 174763 bit / 32000 bit/s ≈ 5.46134375 s.

Rate: 100 000 bit/s

Time: T = 174763 bit / 100 000 bit/s = 0.174763 s.

As we can see, the transmission time decreased 6 times.

Rate: 32 Kilobit/s = 32000 bit/s

Time: T = 1 048 576 bit / 32000 bit/s = 32.768 s.

Rate: 1 megabit/s = 100 000 bit/s

Time: T = 1 048 576 bit / 100 000 bit/s = 1.048576 s.

After compression:

Size: 1 048 576 bit / 6 = 174762.(6) bit = 174763 bit

Rate: 32000 bit/s

Time: T = 174763 bit / 32000 bit/s ≈ 5.46134375 s.

Rate: 100 000 bit/s

Time: T = 174763 bit / 100 000 bit/s = 0.174763 s.

As we can see, the transmission time decreased 6 times.

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