CAT 2025 Lesson : Number Systems - Conversion to other Bases

4. Conversion from Decimal to a different base

To convert a number from base $10$ to base b, successively divide the number by b till we get a quotient of $0$.

The remainders from bottom to top are the digits of the number (in base b) from left to right.



In case you want to verify if your answer is correct, you can convert it back to base $10$.
$(1013)_{8} = (1 \times 8^{3}) + (0 \times 8^{2}) + (1 \times 8^{1}) + (3 \times 8^{0}) = 512 + 8 + 3 = 523$