PS/2 Keyboard Interface

I have a PS/2 keyboard that I want to interface with my Z80 microprocessor. I currently have only a 32K ROM which I am only accessing 256 Bytes of on the memory side, and a UART which is accessing the bottom three address lines A0, A1, and A2 on the I/O side. I am currently able to talk to the UART, and send data over a serial connector on my Desktop PC to see using PuTTy. I understand that the PS/2 keyboard sends out scan codes via a serial interface, and not ASCII values. I would guess that I could hook it up to a micro controller to read the scan codes and convert that to ASCII values then send the ASCII data to the Z80 and finally send this out the UART. Is there any other method? I know there is a PIO chip for the Z80, could I do anything with that?

My end goal with this small chunk of work is to just be able to type characters in on the PS/2 keyboard, and see them on the PuTTy terminal with the Z80. If anyone has a better idea I am open to options. Thanks.