Find the sum and product of each of these pairs of numbers. Express your answers as a base 3 expansion.a) (112)3, (210)3________________b) (2112)3, (12021)3________________c) (20001)3, (1111)3________________d) (120021)3, (2002)3
Solution:Step 1:Addition algorithmAssume two expansion p and q with base 3 with n turns P = ()Q = ()To add p and q , first add their rightmost digits+Hence, is the rightmost digit in the expansion of p +q and is the carry where 0.Continue this process till +Thus p+q = (By using this algorithm be try to solve the questionsStep 2:Algorithm for multiplication Let us consider two sets p and q with base 3 in terms of m are p= (), q = ()By using the distribution law to multiply p and qPq = a(q030 + q131 +q232+ ….qn-13n-1)Then, (pq)i3i with the shift of the expansion of abi i places to the left and add j 0 at the tail end of the expansion.Finally pq by the sum abj3j , j = 0,1,2,3,,....n-1Step 3:a). Sum of (112)3, (210)3 b). Product of (112)3, (210)3 (112)3* (210)3 000 112* 1001**Product of (112)3, (210)3 is (101220)3
