Execution of the laboratory work

1. Study the basics of DL representation including the performance of multiplication and addition operations using this coding.

2. Input into the PC the following subroutines:

• transformation from decimal to DL representation;

• multiplication of two operands in DL representation;

• sorting of an array of partial products in the order of decreasing;

• collecting terms in the ordered array of partial products.

3. Input into the PC two multiplicands; compute their product using a PC and a DL representation algorithm. To compare the precision of the results, transform the former one into DL representation.

Contents of the Experimentation Paper

1. A realization of multiplication with the results obtained:

• transformation of the multiplicands to DL representation;

• the products obtained using a PC and a DL algorithms in DL codes;

• comparing the precision of the results.

2. Conclusions on the work (which of the algorithms are more precise, positive and negative features of processing using DL representation).

Questions for the Self-Testing

1. What is the error of multiplication of two binary digits equal to if the word lengths are 8, 16, 32 bits?

2. What is the data variation range of binary digits whose word lengths are 8, 16, 32 bits?

3. What is the data variation range of DL represented data whose word lengths are 8, 16, 32 bits?

4. What is the increase factor of the data variation range in the case of DL representation compared to the traditional one for word lengths of 8, 16, 32 bits?

Laboratory work 1.2 a study of a systolic processor module using the simulation modeling method

Aim of the work: The work is aimed at gaining practical experience in designing of simulation models.

Basic Principles

The method of simulation modeling consists in representation of structure-functional properties of the object or process under study. From this point of view, the more detailed the simulated object is, the more accurately the processes of its functioning will be investigated. Systolic structures are one of the best examples of realization of the multitask operation principle and are the fundamentals of many high-performance computers and systems.

Simulation models are designed by the following:

• a structure-functional description of the object (process) is drawn up (if possible) on the level of elements or subsystems;

• the functioning of the model components is realized in real or pseudo-real time;

• the characteristics of each model component should be the same as in the real object.

For one-level structure, shown in Fig. 1.1, the following simulation model may be designed:

y ₁ = x₁ V x₂, y₂ = x₁ Λ x₂.

By specifying definite sets of input signals, we can determine the model’s workability and the functional characteristics of the structure.

Execution of the laboratory work

1. Make a careful study of the components systolic processor modules are realized with.

2. Present the results of your home-work on determining the function of two variants of the processor module and your design of the structure-functional model at the level of logic elements.

3. Input into your PC a model description written in a high-level programming language.

4. Using a random number generator, generate a series of input signals for each module.

5. Get code combinations for each level of signal transformation.