Final answer:
To send a 4 Mbits file over a network with a message size limit of 1000 bits, including a 16-bit control field, you would need to send a total of 4,263 messages to transmit the entire file.
Step-by-step explanation:
To send a file of 4 Mbits (megabits) over a network with a maximum message size of 1000 bits, we first need to convert the file size into bits, if it isn't already. Since 'M' in computer data typically stands for 1024², a 4 Mbits file is equal to 4 x 1024 x 1024 bits, which is 4,194,304 bits. However, each message also includes a 16-bit control field, so the total usable data per message is 1000 - 16 = 984 bits.
To find the number of messages required, divide the total file size by the usable data per message:
\(\text{Number of messages} = \frac{4,194,304 \text{ bits}}{984 \text{ bits per message}}\)
Performing the calculation:
\(\text{Number of messages} = 4,262.94\)
Since you can't send a fraction of a message, you would need 4,263 messages to send the complete file.