what is the difference between motherboard speed and the processor speed for computers such as the 80386DX

Your use of the term "motherboard" speed is outdated. I assume you mean motherboard bus speed. Processor speed can be higher than that, and normally, it is a fixed integer speed multiplier, say like 16x, fixed multiple. On the 80386DX, all the variants clocked the bus speed the same as the processor. One version did this all the way up to 40Mhz. So the fixed muliplier was 1:1 on that chip series. The 386 did not offer much improvement over the 286, but the 386 did allow graphical user interfaces on Windows, which is now standard.

To understand the difference between the motherboard bus speed and the processor speed, let's break it down:

1. Motherboard Bus Speed: The motherboard bus speed, also known as the front side bus (FSB), refers to the speed at which data is transferred between the processor and other components on the motherboard, such as memory and expansion cards. It serves as an interface that allows communication between different parts of the computer.

2. Processor Speed: The processor speed refers to the clock speed of the central processing unit (CPU) in the computer. It indicates how many instructions the CPU can execute per second, measured in megahertz (MHz) or gigahertz (GHz). A higher processor speed generally indicates a faster CPU and better performance.

Now, back to your specific example of the 80386DX processor. The 80386DX had a fixed multiplier that determined the relationship between the motherboard bus speed and the processor speed. In this case, the bus speed and processor speed were the same, meaning they operated at a 1:1 ratio. For example, if the bus speed was 40 MHz, the processor speed would also be 40 MHz.

It's worth noting that modern computer systems may have different bus speeds and processor speeds. The bus speed is typically slower than the processor speed, as it needs to accommodate the transfer of data between various components. The processor speed, on the other hand, represents the CPU's processing power.

In summary, the motherboard bus speed refers to the speed at which data is transferred between components, while the processor speed indicates the clock speed of the CPU and its processing capability.