What IC shoud I use if I want to control 136 LEDs using the USB port from a computer?

That'd be plural -- and then some -- which IC*s* are you going to need?

Unless you buy some kind of off-the-shelf USB controlled I/O device, you've first got a problem with the USB. You need a chip (or chips) that will handle the USB signal and interpret it. If you've never written code for USB, you also have a substantial learning curve as you figure out how to write that code for the host (computer) side to drive these LEDs. An off-the-shelf solution might make that a lot easier as well.

Using the nature of your question as an idea for your experience, here's what I'd suggest to you:

With the right multiplexing arrangement, you can control your 136 LEDs (actually, up to 256 of them) with 8 bits. So we're going to be looking for a USB Digital I/O "DAQ" module with at least 8 bits of digital output. Many of these modules use relay outputs, and that really isn't appropriate for this job -- we'll be happy with electronic switching. We also don't need the cost overhead of A/D or D/A, but many of them include that, and it may be cheaper just to have it and not use it.

The device below is a bit of overkill, but at a very decent price. It provides 24 lines of DIO, and we only need 8, but your design will be likely be easier with the 24. There's no way you could begin to build this and write any code for it for $99.


You now take those 24 outputs from the device you bought, and stuff the those in groups of into the inputs of 74LS154 "4 line to 16 line" demultiplexer chips. I believe It'll take one inverter to get you all the decoding you need.

Even the old family 74154 (non-LS) doesn't have enough package dissipation to handle 16 LEDs at any reasonable brightness (only 170mW), so you'll need to back-end the 74LS154s some chips to drive those LEDs at a good current. A pile of 7406 chips should allow you to drive 6 LEDs at a time without cooking.
That depends on what you
want the LED's to do.
depends on what you want the LEDs to do

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