Clock arithmetic
Definition
Clock arithmetic, also known as modular arithmetic, is a system of arithmetic for integers where numbers wrap around after reaching a certain value, the modulus. It is often visualized using the numbers on a clock face where, for example, 13 o'clock is equivalent to 1 o'clock in modulo 12.
5 Must Know Facts For Your Next Test
- In clock arithmetic with modulus n, any integer can be reduced to a number between 0 and n-1.
- Addition and multiplication operations in clock arithmetic are performed by adding or multiplying numbers and then taking the remainder when divided by the modulus.
- Clock arithmetic is fundamental in number theory and has applications in cryptography and computer science.
- If two numbers have the same remainder when divided by the modulus, they are considered congruent modulo that modulus.
- The notation 'a ≡ b (mod n)' denotes that a and b leave the same remainder when divided by n.
Review Questions
- What is 17 mod 5?
- Explain how you would calculate (7 + 9) mod 12.
- Why are numbers like -3 relevant in modular arithmetic?
"Clock arithmetic" appears in:
Related terms
Modulus: The fixed number at which values reset or wrap around in modular arithmetic.
Congruence: A relationship indicating that two numbers have the same remainder when divided by a given modulus.
Residue: The remainder left after division of one number by another.
