Machine Cycle and Crystal Frequency

A machine cycle is the time taken by a computer's CPU to fetch and execute one instruction. It consists of several smaller steps, including fetching the instruction from memory, decoding it, executing it, and storing the result. The duration of a machine cycle is determined by the clock speed of the CPU, which is defined by the frequency of a crystal oscillator.

Crystal frequency refers to the rate at which a quartz crystal vibrates when an electric field is applied to it. This vibration is used to generate a precise and stable signal that is used as the clock signal for a computer's CPU. The frequency of the crystal oscillator is measured in Hertz (Hz) and is directly related to the speed of the CPU.

Calculating Machine Cycle Time

To calculate the time taken by one machine cycle, we need to use the following formula:

Machine Cycle Time = 1 / (Crystal Frequency * Number of Clock Cycles per Instruction)

In this formula, the crystal frequency is measured in Hertz, and the number of clock cycles per instruction is a property of the CPU architecture. For example, some CPUs require two or more clock cycles to execute a single instruction, while others may require only one clock cycle.

Given that the crystal frequency is 20MHz (20 million Hz), we can calculate the machine cycle time as follows:

Machine Cycle Time = 1 / (20,000,000 * 1) = 0.00000005 seconds

This value is in seconds, so we need to convert it to microseconds (µs) by multiplying by 1,000,000:

Machine Cycle Time = 0.00000005 * 1,000,000 = 0.05 µs

Therefore, the time taken by one machine cycle if the crystal frequency is 20MHz is 0.05 µs, which is equivalent to 0.60 microseconds (rounded to two decimal places). Therefore, the correct answer is option B.