Question

please give very detailed explanation

3. For each expression a modn, find an integer b such that b = a mod n and o <b<n. (a) 77 mod 12. (b) -96 mod 7. (c) 1001 mod 3.

Answer 1

Theory:

In computing, the modulo operation finds the remainder after division of one number by another (called the modulus of the operation). Given two positive numbers, a and n, a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is thedividend and n is the divisor.

floor is an rounded near value of divisor.

Examples:floor(2.7)=2 , floor(-3.7)=-4

The formula to calculate a mod b is = a - b × floor(a/b) (*)

a)77 mod 12 = 77 - 12 × floor(77/12)

=77-12×6

=77-72

Ans =5

b)-96 mod 7 = -96 - 7 × floor(-96/7)

=-96-7*(-14)

=-96+98

Answer =2

c)1001 mod 3 = 1001 - 3 × floor(1001/3)

=1001-3*(333)

=1001-999

Answer =2