The digital bin offered by Concept Design (who developed it), Tapematic, and a few others is merely a computer that takes an analogue signal and converts it to digital data stored in banks of high-speed chips. In the mid-1980s this was very new and expensive, and today we take it for granted. During high-speed duplication the data are converted back to an analogue signal whose frequencies are multiplied by a factor of 80. This analogue signal is sent down to a line of no more than ten slave duplicators recording tape at a 80 times faster than cassette playback speed.
(Although this was called a "duplication" system, it is technically a "replication" system because analogue copies can only be replicas of a master. When CD production became popular, it was called "replication" when, in fact, it was digital duplication because digital copies are exact duplicates of the original. Few people in the industry, unfortunately, were linguists.)
The reason that this system was so superior to the previous system of using a bin master tape recorded at 3.75 ips was that copying tape to tape doubles the inherent problems of tape. A sudden peak signal on any tape shows up on an oscilloscope as a peak with signal modulation "skirts" on either side of it. This is extra, unwanted energy. Noise is doubled, so there are an extra 3 decibels of tape noise on the master tape that also gets copied. All this extra signal baggage gets recorded onto a cassette tape and drives up the total flux energy through the recording head and onto the tape. Eliminating the excess energy allows these massive heads and the tape to handle sudden peaks with less threat of distortion as long as the peaks are distinct enough to avoid driving up the total energy onto the tape.
Richard Clark of Concept Design noticed this improvement immediately and asked why he got such high signals on ferric tape without the distortion overload he was used to from ferric bin tape and, to a lesser degree, with BASF chrome 921. It turned out to be chiefly the factor described above plus the fact that he was getting clean masters from the studios.
Recording from a CD or other digital medium to cassette tape can theoretically produce the same results. There are differences, however, that may make the results less impressive.
1) Although the CD/SACD/DVD-Audio disc is a digital source, the content may not be the best. Many of the original CDs were mastered from sub-masters equalized for the flaws in vinyl pressings as studios rushed to pump out as much content as possible in the shortest time possible. These CDs sounded did not sound good, but it was not the fault of the medium; it was the fault of the master and the greed and negligence of the studios. Specialty Records/Allied Records, the production arm of WEA - Warner/Electra/Atlantic -adopted digital bins almost immediately and insisted on high quality masters. That is one reason why their "Digalog" cassettes still sound excellent today. Yet even today there are still CDs produced from digital masters that have the signal levels increased to the maximum with little or no dynamic range. Such CDs cannot produce peak levels at +10 dB on any cassette tape except a metal tape, but that isn't needed for such content because even recording at -10 dB will cover any tape noise. There are simply no dynamics in that kind of recording.
2) The record heads on a duplication slave are massive, some almost the size of a fist. They can take a lot of current before producing distortion artifacts that can get transferred to tape. The physical limits of cassette record heads, even the Nakamichi heads, pose some compromises.
A good, clean digital source with a lot of dynamic range and clean peaks should produce a reasonable approximation of a digital bin on a cassette deck with a good record head that resists overload.