2.5 Modular Arithmetic

In a clock, we use the numbers to to represent the time period of hours. How is it possible to represent the hours of a day in a number format? We use , , , , , , , , , , , and after , we use instead of and instead of and so on. That is after we again start from , , ,...

In this system the numbers wrap around to . This type of wrapping around after hitting some value is called Modular Arithmetic . In Mathematics, modular arithmetic is a system of arithmetic for integers where numbers wrap around a certain value. Unlike normal arithmetic, Modular Arithmetic process cyclically.

The ideas of Modular arithmetic was developed by great German mathematician Carl Friedrich Gauss , who is hailed as the “Prince of mathematicians” . Examples . The day and night change repeatedly. .

The days of a week occur cyclically from Sunday to Saturday. . The life cycle of a plant. .

The seasons of a year change cyclically. (Summer, Autumn, Winter, Spring) . The railway and aeroplane timings also work cyclically. The railway time starts at : and continue.

After reaching : , the next minute will become : instead of : . Fig. .