BECE Mathematics 2022 Theory — Question 2

Model answer

Step 1: change 342_five to base ten. 342_five = 3 × 5² + 4 × 5 + 2 = 75 + 20 + 2 = 97 Step 2: change 97 to base two by dividing by 2: 97 ÷ 2 = 48 r 1 48 ÷ 2 = 24 r 0 24 ÷ 2 = 12 r 0 12 ÷ 2 = 6 r 0 6 ÷ 2 = 3 r 0 3 ÷ 2 = 1 r 1 1 ÷ 2 = 0 r 1 Read the remainders from the bottom up: 1100001. Answer: 342_five = 1100001_two