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This answer is based on the assumption that multi-processing describes the ability to seemingly execute multiple tasks at the same time. This is more commonly known as multi-tasking:

First, no software actually slows down a computer, unless special hardware exists that actually affects the CPU hardware. While this is common in modern battery-powered devices, this question is understood to be concerned with the perceivedslowing down of a computer due to use of multi-tasking.

Multi-tasking allows the simultaneous execution of several tasks. Subject to hardware support, these tasks might actually execute simultaneously (on a multi-core or multi-processor system), or might seemingly execute simultaneously due to the use of some form of a time-based multiplex scheme in which each tasks gets a share of the available processing power. In most modern computer systems, a combination of true parallel and seemingly parallel execution is used.

However, additional administrative overhead exists to manage the time-sharing of a single processing unit, or to manage the sharing of other system-wide resources (such as access to global memory, a shared hard disk drive, etc). As a result, duplicating the raw computing power, for example by comparing a system using two identical CPUs with on that uses four of the same, does not double the system's overall performance.

Therefore, you could argue that a computer system which devotes all its capacity to solving problem A will take time TA to do so. A twice as strong computer system solving problems A and B may take more than time TA to solve each, and is thus seemingly slowing down.

The performance gain in this hypothetical example depends on the hardware and software architecture that governs and manages the shared resources, and on the running tasks' nature. In real life terms however, most "parallel task" are idle most of the time, as they wait on input from a human, wait for slow peripheral devices such as hard disk drives or network transactions to complete, etc.

You can therefore argue that multi-tasking actually increases the perceived speed of execution, since the system can devote most of its processing power to solving problem A while problems B, C and D await completion of slower peripheral tasks or user input. The system thus appears able to solve problems A, B, C and D, while the single-minded system devoted to one problem at a time could only solve problem A in approximately the same time.

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Q: How does multi-processing slow down a computer?
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