Modular Arithmetic

hotshot can always say, it is 7.00 p.m. and the same feature can be also rove as itis 19.00 . If the truth underlying these cardinal statements is understood well, one hasunderstood standard mathematics well.The conventional arithmetic is ground on gunstockar number trunk known as the number line. Modular Arithemetic was introduced by Carl Friedrich Gauss in 1801, in his book Disquisitiones Arithmeticae. (modular). It is ground on circle. A circle can be dissever into each number of parts. Once divided, each(prenominal) part can benamed as a number, just like a clock, which consists of 12 divisions and eachdivision is numbered progressively. Usu solelyy, the scratch line point is named as 0. So,the starting signal point of a set of amount on a clock is 0 and not 1. Since thedivisions are 12, all integers, positive or negative, which are multiples of 12, entrustalways be corresponding to 0, on the clock. Hence, number 18 on a clockcorresponds to 18/12 . hither the counterpoise is 6, so the declaration of 13 + 5 get out be 6Similarly, the same number 18, on a circle with 5 divisions bequeath manufacture number3, as 3 is the curiosity when 18 is divided by 5.Some examples of appendage and multiplication with mod (5)1) 6 + 5 = 11. right off 11/5 gives remainder 1. Hence the answer is 1.2) 13 + 35 = 48. Now, 48/5 gives 3 as remainder. Hence the answer is 3.3) 9 + ( -4) = 5. Now 5/5 gives 0 as remainder. Hence the answer is 0.4) 14 + ( 6 ) = 8 . Now 8/5 gives 3 as remainder. So the answer is 3.Some examples of multiplication with mod ( 5 ).1. 6 X 11 = 66. Now, 66/5 gives 1 as remainder. So the answer is 1.2. 13 X 8 = 104. Now 104/5 gives 4 as remainder . So the answer is 43. 316 X 2 = -632. Now, 632/5 gives 2 as remainder. For negative come the computer science is anticlockwise. So , for negative numbers, theanswer will be numbers of divisions (mod) divided by the remainder.Here the answer will be 3.4. 13 X 7 = 91. Now, 91/5 gives 1 a s remainder. But, the answer will be5 1 = 4. So the answer is 4.Works-cited summon1. Modular, Modular Arithmetic, wikipedia the resign encyclopedia, 2006,Retrieved on 19-02-07 from http//en.wikipedia.org/wiki/Modular_arithmetic2. The entire explanation is based on a web page operable at , http//www.math.csub.edu/faculty/susan/number_bracelets/mod_arith.html spare information An automatic calculator of any type of operations with anynumbers in modular arithmetic is available on website http//www.math.scub.edu/faculty/susan/faculty/modular/modular.html