Binary to Decimal Converter

What Is the Binary Number System?

The binary number system uses only 0 and 1. Each digit has a place value based on a power of 2. Computers use binary to store and process data, so students meet it in computer science, digital technology, and programming.

What Is the Decimal Number System?

The decimal number system uses ten digits, from 0 to 9. Each digit has a place value based on a power of 10. People use decimal for everyday numbers, school math, measurements, prices, and normal calculations at home and school.

How to Convert Binary to Decimal Manually

You can convert binary to decimal by giving each digit a power of 2, multiplying, then adding the results. The rightmost digit starts at 2⁰. Move left and raise the power by one. For example, $10110 = 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 22$. For each step, multiply the binary digit by its power, then add every value. This method gives the decimal equivalent and makes your work easy to check. It also works when you need to explain your answer in class.

Method 1: Using Positions

1. Write the binary digits from left to right.
2. Start with 2⁰ under the rightmost digit.
3. Move left and increase the power by one.
4. Multiply each digit by its power of 2.
5. Add all the products to get the decimal value.

Example: $1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13$.

Method 2: Double Dabble

1. Start with the binary digits.
2. Shift the digits one place at a time.
3. Adjust each decimal digit when it reaches 5 or more.
4. Continue until every binary digit has moved through the process.
5. Read the final decimal digits.

Double dabble works well for digital systems that need decimal digits from binary input.

Unsigned vs Signed (Two's Complement) Results

Unsigned binary treats every bit as a positive value. For example, $1101 = 13$. Signed two's complement uses a chosen bit width, so the same bits can represent a negative value. With 4 bits, $1101 = -3$. Always check whether the result uses signed or unsigned binary.

Binary to Decimal conversion table

Note: Use this table for quick checks. It shows common binary values beside their decimal equivalents, so students can verify practice work in seconds.