11. Base Conversion Basics
Free study material · concepts, shortcuts & solved questions
Although base conversion is not a heavily-weighted topic in SSC/RRB (it appears occasionally, mostly in SSC CGL Tier-2 or as an easy standalone question), it is worth knowing the two basic conversions.
Converting from base 10 to another base (say base b): Divide the decimal number successively by b, noting the remainders at each step. The base-b representation is the remainders read from bottom (last) to top (first).
Converting from another base to base 10: Multiply each digit by b raised to its positional power (starting from 0 at the rightmost digit) and add.
Why it works: Every number system is simply a different “grouping size.” Base 10 groups in tens; base 2 groups in twos; base 8 in eights, and so on. Repeated division by b peels off one “digit” of the new base at a time (the remainder), exactly the reverse of how positional multiplication reconstructs the decimal value.