A processor is the rough equivalent of the pre-frontal cortex of a computer. As the name implies, it is a computer chip that processes all of the information and data that is put through the machine, and may distribute this data to other parts of the machine for further processing.
Essentially, it handles most of the computing, or "thinking", of a computer.
Also known as a CPU, or Central Processing Unit, although this acronym is commonly misused to refer to the entirety of the computer itself excluding the peripherals.
A processor is the logic circuitry that responds to and processes the basic instructions that drive a computer.
The term processor has generally replaced the term central processing unit (CPU). The processor in a personal computer or embedded in small devices is often called a microprocessor.
CPU speed is not a reliable indicator of CPU performance.
Many factors inside and outside of the CPU exert a significant impact on CPU performance, and on overall system performance.
CPU speed is measure in megahertz. A 1MHz CPU can accomplish one million CPU cycles in one second.
Does this mean that a 2MHz CPU is twice as fast as a 1Mhz CPU?
Not necessarily. This depends on how much work each CPU accomplishes in each clock cycle.
The 1MHz CPU might very well be faster, in practice, than the 2Mhz CPU – if it is more efficient or can process more tasks in each CPU cycle.
The purpose of a cache is to enable the CPU to access recently used information very quickly.
A cache will significantly affect CPU performance.
However, caches also represent some difficulties in simple comparison.
Some caches are bigger than others. A typical L1 cache is 256Kb and a typical L2 cache is 1MB.
Generally speaking, the larger the cache, the better the system performance boost. However, this is not always the case.
A cache operates at a certain speed, just like the core of the CPU. Some caches operate at the full speed of the CPU, while others operate at half that speed or less.
A small cache which operates at full speed may be much more useful than a cache which is twice as large but operates at only half the speed of the CPU.
Even comparing cache sizes can be difficult. Some CPU's utilize inclusive caches. In a CPU with an exclusive cache, the data stored in the L1 cache is often duplicated in the L2 cache. Only CPUs which employ exclusive caches will have the full capacity of their L2 caches available.
The Front Side Bus
The Front Side Bus (FSB) is the connection between the CPU and system memory.
The Front Side Bus operates at a speed which is a percentage of the CPU clock speed.
The faster the speed at which the Front Side Bus allows data transfer, the better the performance of the CPU.
RAM has an access speed. Faster RAM will mean the CPU has to wait less often for data. This will, effectively, make the CPU faster.
The Rest of the System
Everything in the system affects total system performance, from the rotational speed and access time of the hard disk drive to the speed of video RAM.
The next possible answer for measuring CPU speed and overall system performance is benchmarking.
Unfortunately, benchmarks are necessarily flawed. A benchmark can only prove how quickly a system runs the benchmark. A benchmark cannot show how quickly a system will run your mix of applications in the real world.
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All your questions can be answered by wiki entries and the general internet so I'm unsure why you are asking such things in a forum. X86 is an instruction set. Read the CPU article to understand speed (frequency).