Here are some of the most important formulas for solving number system aptitude problems:

S.No	To Calculate	Formulas
1.	Decimal to Binary Conversion	To convert a decimal number to binary, divide the decimal number by 2 repeatedly and note the remainders in reverse order.
2.	Binary to Decimal Conversion	To convert a binary number to decimal, multiply each digit by its positional value and sum the results.
3.	Decimal to Hexadecimal Conversion	To convert a decimal number to hexadecimal, divide the decimal number by 16 repeatedly and note the remainders in reverse order.
4.	Hexadecimal to Decimal Conversion	To convert a hexadecimal number to decimal, multiply each digit by its positional value and sum the results.
5.	Binary Addition	Perform addition of binary numbers following the rules of binary addition: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10 (carry 1, write 0).
6.	Binary Subtraction	Perform subtraction of binary numbers following the rules of binary subtraction: 0 – 0 = 0, 1 – 0 = 1, 1 – 1 = 0, borrow from higher place value if necessary.
7.	Binary Multiplication	Perform multiplication of binary numbers following the rules of binary multiplication: 0 × 0 = 0, 0 × 1 = 0, 1 × 0 = 0, 1 × 1 = 1.
8.	Decimal to Binary Conversion	To convert a decimal number to binary, divide the decimal number by 2 repeatedly and note the remainders in reverse order.
9.	Binary to Decimal Conversion	To convert a binary number to decimal, multiply each digit by its positional value and sum the results.
10.	Decimal to Hexadecimal Conversion	To convert a decimal number to hexadecimal, divide the decimal number by 16 repeatedly and note the remainders in reverse order.