Question

Find the sum and product of each of these pairs of numbers. Express your answers as a base 3 expansion. Hint: We can just add and multiply using the grade-school algorithms (working column by column starting at the right), using the addition and multiplication tables in base three (for example, 2 + 1 = 10 and 2 · 2 = 11). When a digit-by-digit answer is too large to fit (i.e., greater than 2), we "carry" into the next column. (10 points) (112)3, (210)3

Answer 1

Answer:

$112_3 + 210_3 = 1022_3$

$112_3 \times 210_3 = 101220_3$

Explanation:

To find the sum of the two numbers, start summing from the right most numbers.

right most: 2 + 0 = 2

middle: 1 + 1 = 2

left: 1 + 2 = 3. Converting 3 to base 3, we have 1 r 0 = 10.

Therefore, $112_3 + 210_3 = 1022_3$.

To find the product, simply do

$(0 \times 112) + (1 \times 112) + (2 \times 112)$ = $000 + 112 + 1001$ = $101220$.