Basic Formulas of Number System
Here are some of the most important formulas for solving number system aptitude problems:
S.No  To Calculate  Formulas 

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. 

Binary to Decimal Conversion 
To convert a binary number to decimal, multiply each digit by its positional value and sum the results. 

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. 

Hexadecimal to Decimal Conversion 
To convert a hexadecimal number to decimal, multiply each digit by its positional value and sum the results. 

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). 

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. 

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. 

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. 

Binary to Decimal Conversion 
To convert a binary number to decimal, multiply each digit by its positional value and sum the results. 

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. 
Quick Tip: Do you know? You can learn number system formulas quickly if you first understand the fundamental concepts of number system.
FAQsFAQs
How do you benefit from learning number system formulas?
One of the significant benefits of understanding number system formulas is the capability to quickly and accurately address simple formulabased questions.
How to remember number system formulas for a longer time?
Following are the techniques you can use to memorise number system formulas:
For a start, you can start understanding the concepts of the number system. It will help you find out why a formula is used.
Keep a separate piece of paper and write down each formula on the number system topic you need to memorise.
Write down and examine each number system formula, but this time with intervals. Write the equation, then take a 2minute break to thinkabout it before writing it again.
Your memory is more likely to associate with the formula you want to remember if you use it more often. Solve the problems employing the formula.
Visualise and repeat out loud the formula occasionally. Create number system formulas flashcards to help with this. You can also use these flashcards while practicing the number system questions.
The formula should be written down and posted somewhere you will see daily. They'll be subconsciously imprinted into your memory.
How conceptual understanding of number system topic helps in remembering its formulas?
Conceptual understanding will help you to make sense of the number system formulas. Conceptual understanding is concentrated on describing why things happen as opposed to how to make them happen. They help you understand the true motive for employing the number system formulas.