Question

Suppose a multiprogramming operating system allocated time slices of 10 milliseconds and the machine executed an average of five instructions per nanosecond. How many instructions could be executed in a single time slice?

Short answer

50,000,000 instructions

Step-by-step solution

Convert milliseconds to nanoseconds

First, we need to convert the time slice from milliseconds to nanoseconds. There are 1,000,000 nanoseconds in a millisecond. Therefore, a time slice of 10 milliseconds is equivalent to \[10 \, \text{ms} \times 1,000,000 \, \frac{\text{ns}}{\text{ms}} = 10,000,000 \, \text{ns}.\]

Calculate instructions per nanosecond

We are given that the machine executes an average of five instructions per nanosecond.

Compute total instructions in a time slice

Now, multiply the number of nanoseconds in a time slice by the number of instructions executed per nanosecond. \[10,000,000 \, \text{ns} \times 5 \, \frac{\text{instructions}}{\text{ns}} = 50,000,000 \, \text{instructions}.\]

Conclusion

Therefore, the machine can execute 50,000,000 instructions in a single time slice of 10 milliseconds.

Key concepts

Multiprogramming

Multiprogramming is a method used in operating systems to improve CPU utilization by running multiple programs concurrently. The CPU switches between different processes, allowing them to take turns using the CPU resources. This not only keeps the CPU busy but also enhances the performance and efficiency of the system.

In a multiprogramming environment, when one program is waiting for input/output operations, another program can utilize the CPU. This approach reduces idle time and maximizes throughput. The operating system controls this process, ensuring that each program gets its fair share of CPU time using techniques such as scheduling and prioritization.

Multiprogramming is essential for applications that require simultaneous processing of various tasks, making it a critical component of modern computing.

Time Slice

A time slice, also known as a quantum, is a small unit of time allocated to a process running in a multiprogramming operating system. This allocation allows the process to execute on the CPU for a short duration before the control is passed to another process.

Time slices are crucial because they enable the operating system to provide a fair distribution of computing resources to all active processes. By switching between processes at the end of each time slice, the operating system can achieve multitasking, where users perceive that multiple applications are running simultaneously.

In our context, a time slice of 10 milliseconds was used, which determines how long a process can run before it is switched out for another.

Instruction Execution

Instruction execution refers to the process where a CPU carries out the commands of an instruction set provided by software applications. Each instruction specifies an operation for the computer to perform, such as processing data, managing memory, or controlling input/output devices.

The speed of instruction execution is influenced by the CPU's architecture and clock speed. In our example, the CPU executes an average of five instructions per nanosecond. This high rate of execution indicates powerful processing capabilities, enabling the completion of millions of instructions within a short period.

Understanding instruction execution helps in grasping how different tasks are processed and how computing performance can be optimized.

Nanoseconds to Milliseconds Conversion

Converting between different units of time is an important skill in computing, especially when dealing with performance metrics like execution speed and response times. A precise understanding of these conversions ensures that calculations about processing capabilities are accurate.

In computing terms:

• 1 millisecond (ms) equals 1,000,000 nanoseconds (ns).
• This conversion helps translate between very fine granularity time measurements suitable for high-speed CPUs and more general-purpose measures suitable for human-readable contexts.

In our exercise, converting 10 milliseconds to nanoseconds gave us 10,000,000 nanoseconds, a crucial step for determining how many instructions can be executed during a single time slice.