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Yes, but the computer would be very simple : PIC can't work with float, and the fastest reachs only 10MIPS whereas your P4 work with float, can multiply/divide, and reachs many thousand MIPS.
You can, for example, develop single application computuer, as this tetris game : **broken link removed**
PICmicros can work with floating point operations, but you need to implement the routines to do that (or use the routines of AN660 and AN575 from Microchip). The problem is that there are no special floating point instructions inside and the PICs are RISC processors, so you need a lot of program memory to implement floating point routines. Remember the old 8088 80286 and 80386 used in the first PCs, that also don´t have the math coprocessor as the 80486 and Pentiums have.
There are some math coprocessors available to PICs microcontrollers in the web.
Returning to the subject, the PICs are not very fast to implement a PC, but is possible to design a small computer using them. Remember that the its architecture is diferent from the PCs microprocessors. PICs have separated memory programs, have small amounts of RAM, and don´t have address ou data buses (instead have I/O ports). In fact, PICs are complete small computers in a single package. The same occur with other uCs.
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