107 LearnersLast updated on July 10th, 2025
Binary to Decimal Conversion
Numbers can be represented in various numeral systems such as binary, decimal, hexadecimal, and octal. Each system has its own base; for example, binary is base 2, and decimal is base 10. Binary is used in computing and digital electronics, where each digit represents a power of 2. Decimal is the standard numeral system used by most people in daily life. Sometimes we need to convert binary numbers to decimal to make them easier to understand. In this topic, we will learn how to convert binary numbers to decimal.
What is Binary?
Binary is a numeral system that uses only two digits: 0 and 1. It is a base-2 system, which is fundamental in computing and digital electronics. Each digit in a binary number represents a power of 2, with the rightmost digit representing 2^0. Binary is used to perform logical operations and arithmetic in digital circuits.
What is Decimal?
Decimal is a numeral system based on ten digits: 0 through 9. It is a base-10 system and is the most commonly used numeral system in the world. Each digit in a decimal number represents a power of 10. Decimal numbers are used in everyday life for counting, measuring, and performing arithmetic operations.
Binary to Decimal Formula
To convert a binary number to a decimal number, you use the following process: Each digit in the binary number represents a power of 2. Decimal = (bn × 2^n) + (bn-1 × 2^(n-1)) + ... + (b2 × 2^2) + (b1 × 2^1) + (b0 × 2^0) Add all the values together to get the decimal equivalent.
How to Convert Binary to Decimal?
Converting binary numbers to decimal is straightforward using the powers of 2. Each binary digit (bit) is a power of 2, based on its position from right to left, starting at 0. Steps to convert binary to decimal: Write down the binary number. Multiply each binary digit by 2 raised to the power of its position number, starting from 0. Add all the products to get the decimal equivalent.
Binary to Decimal Conversion Chart
When working with numbers, sometimes we use binary and sometimes decimal. We use simple conversions to understand how much a binary number is in decimal. Below is a chart that shows some binary-to-decimal conversions.
Common Mistakes and How to Avoid Them in Binary to Decimal Conversion
When converting binary to decimal, people often make mistakes. Here are some common mistakes to help understand the concepts of conversions better.
Mistake 1
Using the wrong base
People get confused and use the wrong base, such as interpreting the binary system as base 10 instead of base 2.
Mistake 2
Ignoring leading zeros
Sometimes, people might ignore leading zeros in a binary number, which can lead to incorrect calculations. Leading zeros do not affect the value but should be considered in calculations.
Mistake 3
Misplacing powers of 2
People can get confused about the position of powers of 2, leading to improper calculations. For example, placing 2^3 instead of 2^2 for a certain bit.
Mistake 4
Incorrect addition of products
During conversion, people might add the products incorrectly. Ensuring each step is accurate is crucial for the correct result.
Mistake 5
Misunderstanding binary representation
People might misunderstand how binary represents numbers, thinking it works like decimal. Remember, each bit is a power of 2, not 10.
Binary to Decimal Conversion Examples
Problem 1
Convert 1101 to decimal
1101 in binary is equal to 13 in decimal.
Explanation
Using the powers of 2: (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 8 + 4 + 0 + 1 = 13
Problem 2
Convert 101011 to decimal.
Solution: Converting 101011 to decimal gives us 43.
Explanation
Use the powers of 2: (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0) = 32 + 0 + 8 + 0 + 2 + 1 = 43
Problem 3
A digital signal represents 11100 in binary. What is it in decimal?
The digital signal in decimal is 28.
Explanation
Convert 11100 to decimal: (1 × 2^4) + (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (0 × 2^0) = 16 + 8 + 4 + 0 + 0 = 28
Problem 4
The value 100111 in binary is what in decimal?
The value in decimal is 39.
Explanation
Convert 100111 to decimal: (1 × 2^5) + (0 × 2^4) + (0 × 2^3) + (1 × 2^2) + (1 × 2^1) + (1 × 2^0) = 32 + 0 + 0 + 4 + 2 + 1 = 39
Problem 5
Converting 1100100 to decimal
1100100 in binary is 100 in decimal.
Explanation
Step 1: Use the powers of 2. (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (0 × 2^3) + (1 × 2^2) + (0 × 2^1) + (0 × 2^0) = 64 + 32 + 0 + 0 + 4 + 0 + 0 = 100
FAQs on Binary to Decimal Conversion
1.How many decimal is 1 in binary?
2.What is 1010 in decimal?
3.Is 11111111 a large number in decimal?
4.How do I convert 110 to decimal?
Important Glossaries for Binary to Decimal Conversion
Conversion: The process of changing one number from one numeral system to another. For example, converting binary to decimal. Binary: A numeral system that uses base 2, consisting of only two digits, 0 and 1. Decimal: A numeral system that uses base 10, consisting of digits from 0 to 9. Bit: A binary digit, which is the smallest unit of data in computing and can have a value of 0 or 1. Power of 2: A mathematical expression representing the number 2 raised to an exponent, used in binary calculations.
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
