Question

Assume that a 1 gigaflop machine is connected to a printer that can print 780 characters per second. In the time it takes to print 1 page ( 65 lines of 60 characters per line), how many floating-point operations can the machine perform?

Short answer

The machine can perform 5 billion floating-point operations.

Step-by-step solution

Calculate Characters on One Page

To find out how many characters are on one page, multiply the number of lines by the number of characters per line. You have 65 lines and 60 characters per line. \( 65 \times 60 = 3900 \) characters per page.

Calculate Printing Time

Given that the printer can print 780 characters per second, compute the time it takes to print 3900 characters (the total number of characters on one page).\( \frac{3900}{780} = 5 \) seconds.

Define Gigaflop

Understand that 1 gigaflop (GFLOP) represents 1 billion (or \( 10^9 \)) floating-point operations per second.

Calculate Floating-Point Operations

Using the gigaflop definition, calculate how many floating-point operations can occur in the time it takes to print one page, which is 5 seconds. Since the machine performs at a rate of 1 GFLOP:\( 1 \times 10^9 \times 5 = 5 \times 10^9 \) floating-point operations.

Key concepts

Gigaflop

Gigaflop is a unit of measurement for computational performance, specifically dealing with floating-point operations. It stands for "billion floating-point operations per second". A floating-point operation is a calculation that involves fractional numbers (numbers with decimal points). These calculations are essential in scientific computations and various applications in engineering and graphics.

• Powerful processing: Gigaflops measure how fast a computer can perform calculations, indicating its raw processing power.
• Scientific importance: Handling tasks like climate modeling or molecular simulations demands high gigaflop counts because these require extensive calculations.
• One gigaflop: Means a computer can handle one billion operations per second.

Understanding gigaflops helps in comparing processing power between different computers or systems, guiding users in making informed choices about technology.

Computational performance

Computational performance refers to the ability of a computer system to efficiently perform tasks and calculations. It is determined by the speed and efficiency of the system in processing data and executing commands.

• Measure of speed: Evaluated by how quickly a computer can process instructions and compute large datasets.
• Importance in technology: High performance allows for faster data analysis, gaming experiences, and the handling of complex algorithms.
• Influence of hardware: Factors like CPU speed, memory capacity, and the number of cores impact computational performance.

To evaluate and benchmark computers, computational performance is often assessed using various standardized tests and metrics, helping to identify the best solutions for specific computing needs.

Printer speed

Printer speed indicates how quickly a printer can produce pages or specific volumes of print jobs. It is usually measured in pages per minute (ppm) or characters per second (cps). Understanding printer speed is crucial for environments requiring fast document production.

• Efficiency: A high-speed printer is essential for offices with extensive printing needs, reducing wait times and enhancing productivity.
• Different metrics: Some printers focus on characters per second, significant for dot matrix or impact printers, while others use pages per minute.
• Impact on workflow: Faster printers can support quicker decision-making processes and more streamlined operations in professional settings.

Evaluating printer speed is part of choosing the right printer for specific tasks, aligning with both personal and professional needs based on required output speed.

Characters per second

Characters per second (cps) is a measure of how many individual characters (letters, numbers, spaces, etc.) can be printed or displayed by a device, typically a printer, in one second. It is an older metric, more commonly associated with dot matrix printers or similar devices where continuous text streams are produced.

• Multiple uses: Not only applies to printers but also to terminal display speeds in computing.
• Relevance: Important when dealing with legacy technology or environments that still use older hardware.
• Understanding speed: Helps in assessing the overall speed of a printer, especially in scenarios where page count might not apply.

Monitoring and knowing characters per second is vital in situations where precise output rhythm matters, ensuring compatibility and usability with anticipated tasks.