Electronics Newbie question concerning LEDs

Yes, you can, but it is a fairly expensive way to drive 160LEDs - you would need an FPGA with at least 160 user I/Os. You would have to go 240pin PQFP (if it has 160 I/Os) or BGA. Multiplexing LEDs in a matrix is much more economic in terms of resources and cost. In the extreme you could do it with 4 + 2 = 6 I/Os! 4 I/Os indicate the column, and is decoded with a 4-16 binary decoder chip. Two I/Os shift the 16 bits for each row into a 16 bit shift register (clock and data). I have done this a long time ago to create a 160 LED matrix and drive it from my PC's parallel port and it worked well.