Question

Файл размером 16 Кбайт передаётся через некоторое соединение со скоростью 2048 бит в секунду. Определите размер файла (в байтах), который можно передать за то же время через другое соединение со скоростью 512 бит в секунду. В ответе укажите одно число — размер файла в байтах. Единицы измерения писать не нужно.

Answer 1

За 64 секунды с такой скоростью удасться передать файл размером:

 

4096 байт

Answer 2

Problem Analysis

We are given a file with a size of 16 kilobytes (KB) that is being transmitted through a connection with a speed of 2048 bits per second (bps). We need to determine the size of the file (in bytes) that can be transmitted in the same amount of time through another connection with a speed of 512 bps.

Solution

To solve this problem, we need to calculate the time it takes to transmit the file through the first connection and then use that time to calculate the size of the file that can be transmitted through the second connection.

Let's start by calculating the time it takes to transmit the file through the first connection.

Step 1: Convert the file size from kilobytes (KB) to bytes. - 1 kilobyte (KB) = 1024 bytes. - Therefore, the file size is 16 KB * 1024 bytes/KB = 16384 bytes.

Step 2: Calculate the time it takes to transmit the file through the first connection. - File size = 16384 bytes. - Connection speed = 2048 bits per second (bps). - 1 byte = 8 bits. - Therefore, the time it takes to transmit the file through the first connection is 16384 bytes / (2048 bits/second * 8 bits/byte) = 1 second.

Now, let's calculate the size of the file that can be transmitted through the second connection in the same amount of time.

Step 3: Calculate the time it takes to transmit the file through the second connection. - Connection speed = 512 bits per second (bps). - The time it takes to transmit the file through the second connection is 1 second (same as the first connection).

Step 4: Calculate the size of the file that can be transmitted through the second connection. - Connection speed = 512 bits per second (bps). - Time = 1 second. - File size = Connection speed * Time = 512 bits/second * 1 second = 512 bits.

However, we need to convert the file size from bits to bytes.

Step 5: Convert the file size from bits to bytes. - 1 byte = 8 bits. - Therefore, the file size is 512 bits / 8 bits/byte = 64 bytes.

Answer

The size of the file that can be transmitted in the same amount of time through another connection with a speed of 512 bits per second is 64 bytes.

Verification

To verify the answer, we can calculate the time it takes to transmit the file through the second connection and check if it matches the time calculated for the first connection.

Verification Step 1: Calculate the time it takes to transmit the file through the second connection. - File size = 64 bytes. - Connection speed = 512 bits per second (bps). - 1 byte = 8 bits. - Therefore, the time it takes to transmit the file through the second connection is 64 bytes / (512 bits/second * 8 bits/byte) = 1 second.

The calculated time matches the time calculated for the first connection, which confirms that the answer is correct.

Conclusion

The size of the file that can be transmitted in the same amount of time through another connection with a speed of 512 bits per second is 64 bytes.