The performance of a computer’s architecture is measured by the time it takes to complete a certain amount of work. Time is usually measured in the following way:

t c = clock cycle time, constant

IC = instruction count (number of instructions needed to complete task)

CPI = average clock cycles per second

Thus, the execution time for a given workload is T = t c*CPI*IC

This value is calculated for an established benchmark task, and the performance is then given by the inverse of the total time required: P = 1/T

The quality of an architectural design depends not only on its performance but also on the cost of performing a task. Depending on the circumstance, cost might describe the market price of an architectural component, or it may refer to computational cost in terms of time. Often, quality is given by the following relation:

Q = P (1-q)/C q,

where q is a parameter which describes whether the performance or the cost has a greater impact on quality (q>0.5 implies that cost is more important).

All architectural design changes cause trade-offs in cost and performance. In the case of the 64-bit processor, varied results are observed in terms of performance. For some tasks, 64-bit processors only marginally increase performance (measured below in frames per second):

In other applications, such as compressing files, 64-bit processing more than doubled the speed of the task:

Source: http://www.pcstats.com/articleview.cfm?articleid=1665&page=6

Finally, it is important to recognize that the presence of a 64-bit processor alone does not guarantee improved performance, especially for certain tasks. Performance depends on an entire architecture, and different computer models may be more efficient than others for reasons unrelated to the bit size of the core processor. The following diagram illustrates this case: