An Approach to Dividing Modules of Numbers by the Values of Bases in Number Systems in Residual Classes


  • Alexey Alexeevich Lyubomudrov
  • Elman Said-Mokhmadovich Akhyadov
  • Elena Victorovna Afanaseva



The paper considers an approach to division modules of numbers by bases in number systems in residual classes (RNS). This may be required when solving specific tasks.
The approach involves performing the following sequence of actions in the RNS:
- reducing the modulus of numbers by the value of the deduction corresponding to the base by which the division is made;
- dividing the reduced module by the value of the base;
- formation the correction value and its addition to the quotient obtained.
In total the division operation is performed through four accesses to the table memory two of which are overlapped in time.
If one of the bases of the RNS is equal to pn then the approach under consideration allows to reduce the capacity of table memory by pn times in relation to the capacity of table memory containing the full set of division results, where pn is the base of the RNS by which the division is performed.