**9. References**

348 Applications of Digital Signal Processing

set is smaller than the second set. Furthermore, the reverse converter for the moduli set {2*n*– 1, 2*n*, 2*n*+1, 2*2n*+1–1} relies on less hardware requirements than others. From another side, the moduli sets {2*n*–1, 2*n*, 2*n*+1, 22*n*+1–1} and {2*n*–1, 2*n*+1, 2*2n*, 2*2n*+1–1} results in faster RNS arithmetic units than the moduli sets {2*n* –1,2*n*, 2*n* +1, 22*n* +1} and {2*n*–1, 2*n*+1, 22*n*, 22*n*+1}.

Operand Preparation Unit 1

<sup>1</sup>*x* <sup>2</sup> *x* <sup>3</sup> *x* <sup>4</sup> *x*

Fig. 4. The converter for moduli set {2*n*–1, 2*n*+1, 2*2n*, 2*2n*+1–1} (Molahosseini & Navi, 2010)

The Residue Number System has been recognized as one of the efficient alternative number systems which can be used to high-speed hardware implementation of Digital Signal Processing computation algorithms. However, forward and reverse converters are needed to act as interfaces between RNS and the conventional binary digital systems. The overhead of these converters can frustrate the speed efficiency of RNS, and due to this a lot of research

(2*n*+1)-bit CPA with EAC

*T*

(2*n*+1)-bit CSA with EAC

Operand Preparation Unit 2

 

*X*

(4*n*+1)-bit CPA 1

*Y*

1*x*

*Y*

<sup>0</sup> 

2*n*-bit CPA with EAC

2*n*-bit CSA with EAC

2*n*-bit CSA with EAC

**8. Conclusion** 


**17** 

*BAE Systems* 

*USA* 

**Entropic Complexity Measured** 

**Abstract**: A complexity metric for concurrent software controlled systems is defined and derived. It is equivalent or comparable to the Shannon information metric, which essentially measures entropy of a system, but uses a novel and efficient technique based on a FFT to calculate its value. This can be extended to other temporal realizations of

For concurrent software, the amount of context switching that occurs indicates the level of complexity of the program. If the program consists of a fixed period cyclic scheduler, context switches will occur very predictably at those same fixed intervals. However, if the program consists of a mix of periods, some long, some short, and some perhaps sporadically aperiodic, the complexity of such a program will be much greater. Further, the greater the spread between short periods and long periods will indicate that the program will be much harder to verify, as the shorter cycles will accumulate more testing coverage than the longer

In some sense, this is what makes clock-driven synchronous logic much easier to test. The state space of possible events is reduced in direct relation to the reduction of available slots for computation. As the context switching and potential interactions between threads occurs only at these slots, a simplification of the temporal behaviour here will result in a better

By the same token, any concurrent program will show greater non-determinism than an equivalent sequential program. The benefits of making a concurrent program more synchronous grants a greater predictability in its execution semantics. In terms of meeting hard real-time constraints, a synchronously designed program will have predictable points for schedulability, allowing for techniques such as rate-monotonic scheduling (Klein, 1993) to meet strict timing deadlines. These categories of techniques grant a concurrent program

Even though these strict scheduling programs are effective for their problem domains, they are difficult to maintain and do not scale that well for the large software systems required. In fact most interactive programs and other soft real-time systems use the concept of eventdriven semantics, which can allow interruption at any point in time. These have the benefit of dealing with interactions only upon demand, and so scale better, especially in terms of not placing a huge computational or communication load on the system when not needed.

**1. Introduction** 

or sporadic interval context switching.

chance to verify the correctness of its execution.

the same possibilities for verification as a sequential one.

behaviour.

**in Context Switching** 

Paul Pukite and Steven Bankes

