WAEC Data Processing 2015 Paper

Concept:Convert the octal number to decimal first, then change the decimal number into binary by repeated division by $2$.Explanation:Write $47_8$ in expanded form using powers of $8$.$47_8 = 4 \times 8^1 + 7 \times 8^0$$= 4 \times 8 + 7 \times 1 = 32 + 7 = 39_{10}$Now convert $39_{10}$ to base $2$.Divide $39$ by $2$ repeatedly and note the remainders.$39 \div 2 = 19$ remainder $1$$19 \div 2 = 9$ remainder $1$$9 \div 2 = 4$ remainder $1$$4 \div 2 = 2$ remainder $0$$2 \div 2 = 1$ remainder $0$$1 \div 2 = 0$ remainder $1$Write the remainders from the last division to the first.This gives $100111_2$.Answer:$47_8 = 100111_2$Therefore, the correct option is A.