I understood that in Cathode 7 segment display. To turn a,b,c,d,e...., you need "HIGH" because they share same ground so that flowing of electricity into specific input will make them turn on. It would work the other way for anode, of course.
But I don't know why it would be again, opposite, for, selecting certain digit. (1st digit(thousands), 2nd digit(hundreds) and so on.)
Consider that it is cathode and 64pin - thousands, 65-hundreds, 66-tens, and 67- one, and you want only thousandth number (1xxx) figure to show up (you need only 64 pin)
I thought you need to make it (64-HIGH, 65- LOW, 66-LOW, 67-LOW) but answer is opposite.
I can't figure out what you are trying to explain in your third paragraph but from the first two I believe you are describing a multiplexed common-cathode 7-segment display.
In such a display the anodes of all of the 'a' segments go to one pin, the anodes of all of the 'b' segments go to another pin, etc.
In that same display the cathodes of all of the segments (a, b, c, ...) of the 'ones' digit go to one pin, the cathodes of all of the segments of the 'tens' digit go to another pin, etc.
The segment selection is done with a high level since you are dealing with the LED anodes. The digit selection is done with a low level since you are dealing with the LED cathodes.