It used to be that if you were recording with a camcorder then you were by default recording onto tape. All domestic cameras used mini dv tapes to record to while at the professional level people used dig beta. Essentially dig beta was a larger tape with a wide magnetic strip to record the image to. This meant that the image that came through the camera had more magnetic molecules from which to draw a picture and thus created a better image (in the same way that 32mm film produces better quality than 8mm film).
Tape pretty reliable and the quality was actually really good. So why change?
1, Capturing (which is the process of getting the video into the computer that you are going to edit on) was a slow and time consuming process if done properly. The person responsible for capturing would have to constantly stop and start as they captured various takes. With digital each separate recording is uploaded to the computer.
2, Some times tape would suffer from drop out, which is when some frames on the tape don't record due to the complex movement of the magnet ribbon within the tape.
Digital does not require the moving parts and therefore is more consistent and reliable.
3, Tapes can only be used so many times before the image quality suffers, where as with a digital card, as long as you look after it will be fine to constantly re use it.
4, Length of a single record with a tape is restricted to the length of the tape, where as with many digital; recording devices one could literally record for 8 hours with out interruption.
All in all there are many advantages to digital memory recording however the cost of digital storage can be expensive at first. Using both tape and digital gives a great insurance in case anything should go wrong with one element of the recording.
This is extremely advantages if for example you were shooting a wedding video, as you simply can not go back and re shoot some ones wedding.
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