What is a single-chip microcomputer?

Here are the main differences:

Single Chip

• Everything is packaged in the same single physical IC
• The IC contains the CPU core(s)
• The IC contains the memory (ROM and RAM)
• The IC contains all the IO hardware (Video, serial, etc)

Single-chip computers are mainly of the form known as Microcontroller chips (the most commonly known are the PIC range by Microchip inc) and used in embedded devices. They provide much more basic functionality but are far simpler to work with as they don't require any external chips in order to function. Some attempts have been made to create single-chip computers of the style of Intel or AMD PC architectures, but due to the complexity of the components involved this has not been a very easy task. Again, these are generally used in low-end embedded systems, such as touch-pad devices and industrial control systems.

Multi-chip

• The CPU IC contains the CPU cores.
• The Video GPU contains the video processor.
• The RAM modules contain the RAM memory.
• The BIOS chip contains the ROM memory.
• The "chipset" (northbridge/southbridge, etc) contains the IO logic and bus interface logic

Traditional computers are Multi-Chip. Some of the most recent processors (some of the i series from Intel) include the video GPU in the processor IC, but they still require external chips in order to interface with the rest of the computer (PCI bridge, etc)

well, more precisely its a system on chip microcomputer - modern computers often have specialised chips and chipsets for particular roles - the northbridge - often integrated in to the processor die, and handing memory control, and certain specialised IO -and southbridge - which handled other IO on previous generations for example. A SOC is really all these specialised components, networking, memory, processor, video and such, crammed into a single chip. The advantage of this is lower cost per chip and lower latency , but with older process sizes, this wasn't possible - the chip would be too big, and you'd have lower yield.

A multiple chip computer might have seperate IO, memory and processing chips on seperate dies and packaging.

An example of a SOC system would be the AMD geode - contrast this with the intel 440 series (yes, its old, but its pretty much the ideal typical old school chipset)