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In a webpage I saved from long time ago:

Many people are happy when they purchase their first scanner because they can now attach images to the Email they send to friends and family. Little do they know that the art of scanning photographs into clear, crisp image files of a small size (50 KB or less) requires skill and an understanding of their scanner hardware and image editing software.

(NOTE: The small file size as given above is recommended because it only requires about 10 seconds to transmit a file of this size through their modem; hence, neither sender nor receiver will grow impatient waiting. The 10 second time is calculated as follows for a typical 56.6 Kbps modem connection: 50 KBytes x 8 bits/Byte / 40,000 bits/sec = 10 sec. The discussion below reveals that if you're not careful, you could easily spend 100 times longer than the above 10 seconds waiting for the file to transmit to the recipient!)

I wonder where "40,000 bits/sec" comes from in the calculation for the time for transmission? it isn't equal to "56.6Kbps". Or am I missing something?

Thanks.

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A 56k modem would virtually never provide a 56k connection due to a whole raft of issues - including impedence mismatch and other cabling faults and hardware incompatibilities. 40-48k seemed to be the norm from memory - connections over 53k were very, very rare.

Also, most modems followed the "V90" standard which was asymetrical and limited upload speeds to 33.6k - not 48k of the "V92" standard.

[ Source: I used to run an ISP in the days of dialup and invested quite heavily in special 56k capable modems - for a 56k connection the ISP could not use a standard modem they needed to use a 64k ISDN channel ].

Also, this whole post is simplistic (you could argue flawed if you want to be pedantic) - That 50kb * 8kbits is naive as it ignores the overheads of sending the file - this is quite significant on an Internet connection but even on a basic connection it was non-trivial - think an overhead of 10%

As someone else has posted, if the image is being sent in an email, there is substantial overhead in converting the file from 8 bits of ASCII per character to something which falls in the acceptable space for email (readable characters, line limits). This could vary by encoding method - there is more then 1, but in the region of 33% overhead.

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I wonder where "40,000 bits/sec" comes from in the transmission calculation?

A 56.6 Kbps modem connection uses V.92.

The upload speed is a max of 48 kbit/s, but at the expense of download rates.

A 48 kbit/s upstream rate would reduce the downstream as low as 40 kbit/s due to echo on the telephone line.


Using digital lines and PCM (V.90/92)

The International Telecommunication Union (ITU) announced the draft of a new 56 kbit/s standard, V.90, in February 1998 with strong industry support.[4] Incompatible with either existing standard,[4] it was an amalgam of both which was designed to allow both types of modem to be converted to it by a firmware upgrade. This V.90 standard was approved in September 1998, and widely adopted by ISPs and consumers.[4] Later in V.92, the digital PCM technique was applied to increase the upload speed to a maximum of 48 kbit/s, but at the expense of download rates. A 48 kbit/s upstream rate would reduce the downstream as low as 40 kbit/s due to echo on the telephone line.

Source Modem

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Normally, the 56600 bps rate should be used in this calculation. However, e-mail attachments typically use base64 encoding where each 3 8-bit bytes are encoded by 4 7-bit ASCII characters, and most e-mail clients can only handle 8-bit characters anyway, so the net result is transforming 3 bytes into 4, and the effective transfer rate will be

56600 / 4 * 3 = 42450 (bps)

PS. As @David's answer points out, a 56.6k modem has its upload speed limited at 48000 bps. Applying the same "correction" for this rate gives

48000/ 4 * 3 = 36000 (bps)

Still, none of these calculations give the exact 40000 bps result, so I suppose it's an approximative value.

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  • Thanks, but why "/4*3"? – Tim Jun 7 '15 at 23:44
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    E-mail attachments typically use base64 encoding where each 3 8-bit bytes are encoded by 4 7-bit ASCII characters, and most e-mail clients can only handle 8-bit characters anyway, so the net result is transforming 3 bytes into 4. – Dmitry Grigoryev Jun 7 '15 at 23:48
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    It might be a good idea to add this explanation to your answer. – MariusMatutiae Jun 8 '15 at 5:53

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