105 LearnersLast updated on July 10th, 2025
Decimal to Binary Conversion
In mathematics and computer science, numbers can be represented in various numeral systems, such as decimal, binary, octal, or hexadecimal. The decimal system is the most commonly used and is based on the number 10, employing digits from 0 to 9. The binary system, however, is based on the number 2, using only the digits 0 and 1. Converting decimal numbers to binary is essential in computing and digital electronics, as computers use binary language to process data. In this topic, we will learn how to convert decimal numbers to binary.
What is Decimal?
A decimal system is a base-10 numeral system, which is the standard system for denoting integers and non-integers. It is the most widely used system in daily life for expressing numbers. The decimal system utilizes ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit's position in a number represents a power of 10, making it straightforward to perform arithmetic operations.
What is Binary?
The binary numeral system, or base-2 system, represents numeric values using two symbols: 0 and 1. It is the foundation of all binary code, which is used in computing and digital systems. Each digit in a binary number represents a power of 2, and the binary system is essential for computer operations and digital circuit design.
Decimal to Binary Formula
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. The binary equivalent is obtained by reading the remainders from bottom to top. Convert the integer part of the decimal to binary by dividing by 2 until the quotient is 0.
How to Convert Decimal to Binary?
Converting a decimal number to binary involves dividing the number by 2 and keeping track of the remainders. The steps are: Write down the decimal number. Divide the number by 2. Record the remainder (0 or 1). Repeat the process with the quotient until it is 0. The binary number is obtained by reading the remainders in reverse order.
Decimal to Binary Conversion Table
When dealing with numbers, we often use decimal and binary systems. Here is a conversion table to help understand how decimal numbers are represented in binary.
Common Mistakes and How to Avoid Them in Decimal to Binary Conversion
When converting decimal numbers to binary, beginners often make mistakes. Here are some common errors to help understand the conversion process better.
Mistake 1
Misunderstanding the division process
Learners sometimes confuse the division process, forgetting to track the remainders properly, leading to incorrect binary results.
Mistake 2
Incorrect order of remainders
Students might list the remainders in the order they are calculated, instead of reversing them to form the binary number. For example, instead of writing the binary for 10 as 1010, they might incorrectly write it as 0101.
Mistake 3
Ignoring the quotient
Some learners overlook the quotient in each division step, stopping the process prematurely, which results in an incomplete binary representation.
Mistake 4
Using subtraction instead of division
Beginners may mistakenly use subtraction instead of division to convert decimal numbers, leading to incorrect binary conversions.
Mistake 5
Misinterpreting powers of 2
Students often confuse the value of binary digits by misinterpreting the powers of 2, affecting the accuracy of binary representation.
Decimal to Binary Conversion Examples
Problem 1
Convert 45 to binary
45 in decimal is 101101 in binary.
Explanation
To convert 45: 45 ÷ 2 = 22 remainder 1 22 ÷ 2 = 11 remainder 0 11 ÷ 2 = 5 remainder 1 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Binary: 101101
Problem 2
Convert 78 to binary.
Solution: 78 in decimal is 1001110 in binary.
Explanation
Convert 78: 78 ÷ 2 = 39 remainder 0 39 ÷ 2 = 19 remainder 1 19 ÷ 2 = 9 remainder 1 9 ÷ 2 = 4 remainder 1 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Binary: 1001110
Problem 3
A device uses the number 256. What is it in binary?
256 in decimal is 100000000 in binary.
Explanation
Convert 256: 256 ÷ 2 = 128 remainder 0 128 ÷ 2 = 64 remainder 0 64 ÷ 2 = 32 remainder 0 32 ÷ 2 = 16 remainder 0 16 ÷ 2 = 8 remainder 0 8 ÷ 2 = 4 remainder 0 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Binary: 100000000
Problem 4
What is 15 in binary?
15 in decimal is 1111 in binary.
Explanation
Convert 15: 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Binary: 1111
Problem 5
Convert 1024 to binary
1024 in decimal is 10000000000 in binary.
Explanation
Convert 1024: 1024 ÷ 2 = 512 remainder 0 512 ÷ 2 = 256 remainder 0 256 ÷ 2 = 128 remainder 0 128 ÷ 2 = 64 remainder 0 64 ÷ 2 = 32 remainder 0 32 ÷ 2 = 16 remainder 0 16 ÷ 2 = 8 remainder 0 8 ÷ 2 = 4 remainder 0 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Binary: 10000000000
FAQs on Decimal to Binary
1.What is the binary of 7?
2.What is 50 in binary?
3.Is 128 a power of 2?
4.How do I convert 64 to binary?
Important Glossaries for Decimal to Binary Conversion
Conversion: The process of changing one number from one numeral system to another, such as from decimal to binary. Binary Number: A number expressed in the base-2 numeral system, using only the digits 0 and 1. Decimal Number: A number expressed in the base-10 numeral system, using digits from 0 to 9. Remainder: The amount left over after division, crucial for determining binary digits. Power of 2: Numbers like 1, 2, 4, 8, etc., which are the result of raising 2 to an integer power.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
