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Modular Arithmetic and Algorithms Calculators

Samuel Dominic Chukwuemeka
I greet you this day,

You may use these calculators to check your answers.
You are encouraged to solve the questions first, before verifying your answers with the calculators.
I wrote the codes for these calculators using Javascript, a client-side scripting language. Please use the latest Internet browsers. The calculators should work.

Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome.
You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you.

Samuel Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

Convert Number Systems

  • Not valid for numbers with decimal points/places.
  • For base two, please enter only 0's and 1's.
  • For base three, please enter only 0's, 1's, and 2's.
  • For base four, enter only 0's, 1's, 2's, and 3's; and so on and so forth.

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Number Systems Arithmetic

Add, Subtract, Multiply, and Divide Number Systems

  • Not valid for numbers with decimal points/places.
  • For base two; please enter only 0's and 1's for the number, and 2 for the base.
  • For base three; please enter only 0's, 1's, and 2's for the number, and 3 for the base.
  • For base four; enter only 0's, 1's, 2's, and 3's for the number, and 4 for the base.
  • The calculation is done for two numbers and two systems at a time.
  • Enter the two numbers and the two systems first.
  • Then, select the base for which you want the answer to be in.
  • Click on the arithmetic operation you want.

in base



in base

=





Division

$Divisor \:\:|\:\: Dividend = Quotient \:\:R\:\: Remainder$

| = R





Modulo

mod =





Greatest Common Divisor

The GCD of and =

Greatest Common Divisor of an Array

=





Least Common Multiple

The LCM of and =

Least Common Multiple of an Array

=





Modular Inverse

The inverse of mod

=





Extended Euclidean Algorithm

GCD and Bezout's Coefficients

  • This calculator returns an array of three answers
  • The first answer is the GCD
  • The other 2 answers are the Bezout's Coefficients

The Extended Euclidean Algorithm of and

=





Linear Congruence

Solve for the variable

$x$ ≡ mod ()

$x$ =





System of Linear Congruences

Solve for the variable

These calculators are for Relatively Prime Moduli only where:

(1.) each modulo is a positive integer greater than $1$
(2.) the coefficient of the variable is $1$
If the coefficient of the variable is not equal to $1$, divide both sides (do not include the modulo) by the coefficient of the variable. This works for relatively prime moduli.

  • Given: a set of 2 linear congruences where the coefficient of the variable is $1$
    To Find: the value of the variable

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ =



  • Given: a set of 3 linear congruences where the coefficient of the variable is $1$
    To Find: the value of the variable

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ =



  • Given: a set of 4 linear congruences where the coefficient of the variable is $1$
    To Find: the value of the variable

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ =



  • Given: a set of 5 linear congruences where the coefficient of the variable is $1$
    To Find: the value of the variable

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ ≡ mod ()

$x$ =





Modular Exponentiation

mod =





Check Digit for ISBN

International Standard Book Number

$\boldsymbol{Example\:1}$ Calculate the check digit of the $ISBN-10: $

Check Digits Calculators

These calculators will not allow you to:
(1.) Type a negative number.
(2.) Type more than a single digit in each text box.
(3.) Delete place holders.

Calculate the Check Digit of an ISBN-10

Given: The 9 Digits of a 10-Digit ISBN
To Find: The Check Digit

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Determine if an ISBN-10 is valid
Convert an ISBN-10 to an ISBN-13

Given: A 10-Digit ISBN
To Determine: If it is valid or invalid
To Convert: To a 13-Digit ISBN

NOTE: If the check digit is an "X", please type the uppercase X (not lowercase x) as is.

-



The converted $ISBN-13$ is:

-





Calculate the Check Digit of an ISBN-13

Given: The 12 Digits of a 13-Digit ISBN
To Find: The Check Digit

-



Determine if an ISBN-13 is valid
Convert an ISBN-13 to an ISBN-10

Given: A 13-Digit ISBN
To Determine: If it is valid or invalid
To Convert: To a 10-Digit ISBN

-



The converted $ISBN-10$ is:

-