1. Evaluate ( 202^2_{three} – 112^2_{three})

1. Evaluate ( 202^2_{three} – 112^2_{three})

Correct Answer: Option A

Explanation

(202^2_{three})when converted to base ten (=(202_3)^2\
202_3 = 2 times 3^2 + 0 times 3^1 + 2times 3^0 = 18 + 0 + 2\
=20_{ten}; (202_3)^2 = (20)^2_{ten} = 400\
112^2_{three})when converted to base ten (= (112_3)^2\
112_3 = 1 times 3^2 + 1 times 3^1 + 2times 3^0 = 9+3+2=14_{ten}\
(112_3)^2 = (14)^2_{ten} = 196_{ten}\
Evaluate Longrightarrow 400-196 = 204)
Reconvert to base three
(begin{matrix}
3 & 204\
3 & 69 &R0\
3 & 22 & R2\
3 & 7 & R1\
2 & 2 & R1\
& 0& R2 uparrow\
end{matrix} \
=21120_3)