Day 06Part 09- Operating System for gate- Arithmetic Modulo- Additive and Multiplicative Modulo

Day 06Part 09- Operating System for gate- Arithmetic Modulo- Additive and Multiplicative Modulo

Day 06 Part 09 – Operating System for GATE

 Arithmetic Modulo – Additive and Multiplicative Modulo

 What is Modulo Arithmetic?

Modulo Arithmetic (also called mod arithmetic) deals with remainders when numbers are divided. It is used in cryptography, hashing, clock arithmetic, and operating systems.

The modulo operation is written as:

$$A\mathrm{mod}B$$

This gives the remainder when A is divided by B.

Example:

$$17\mathrm{mod}5=2$$

(Since $17÷5=3$ remainder 2).

 Additive Modulo

If we add two numbers under a modulo, we use the formula:

$$(A+B)\mathrm{mod}M=((A\mathrm{mod}M)+(B\mathrm{mod}M))\mathrm{mod}M$$

Example:

$$(7+5)\mathrm{mod}4$$

Step 1: $7\mathrm{mod}4=3$, $5\mathrm{mod}4=1$
Step 2: $(3+1)\mathrm{mod}4=4\mathrm{mod}4=0$
 Answer: 0

 Multiplicative Modulo

If we multiply two numbers under a modulo, we use the formula:

$$(A\times B)\mathrm{mod}M=((A\mathrm{mod}M)\times (B\mathrm{mod}M))\mathrm{mod}M$$

Example:

$$(7\times 5)\mathrm{mod}4$$

Step 1: $7\mathrm{mod}4=3$, $5\mathrm{mod}4=1$
Step 2: $(3\times 1)\mathrm{mod}4=3\mathrm{mod}4=3$
 Answer: 3

 Applications in Operating Systems & GATE

Hashing Functions (Used in databases & OS)
Clock Arithmetic (Example: 12-hour clock)
Encryption & Cryptography (RSA Algorithm)
Scheduling Algorithms (Round-Robin Scheduling)

Would you like practice questions or code examples in Python/C++?

Day 06Part 09- Operating System for gate- Arithmetic Modulo- Additive and Multiplicative Modulo

UNIT-II Modular Arithmetic and Cryptography

UNIT- III Modular Arithmetic