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The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
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    Area of Science:

    • Computer Science
    • Information Theory
    • Digital Systems

    Background:

    • Number systems are fundamental for representing numerical data.
    • Efficient digital system conversions are vital for human-computer interaction and data processing.
    • Existing conversion methods can be time-consuming.

    Purpose of the Study:

    • To develop novel SNP (Symbolic Number Processing) systems for number system conversions.
    • To construct SNP systems capable of converting between any two arbitrary number systems.
    • To enhance the efficiency of decimal-binary and binary-decimal conversions.

    Main Methods:

    • Construction of two initial SNP systems for decimal-binary conversion.
    • Generalization to a family of SNP systems for arbitrary number system conversions.
    • Verification of system feasibility and effectiveness through illustrative examples.

    Main Results:

    • The proposed SNP systems demonstrate feasibility and effectiveness.
    • Decimal-to-binary conversion time is reduced to approximately 1/3 of existing methods.
    • Binary-to-decimal conversion time is reduced to approximately 43% of existing methods.

    Conclusions:

    • The developed SNP systems offer a significant improvement in conversion efficiency.
    • These systems have broad applicability in digital information processing.
    • The SNP approach provides a faster and more effective method for number system conversions.