What is binary arithmetic?

Binary arithmetic is math performed in base 2, where the only digits are 0 and 1. Each digit position represents a power of 2, unlike decimal where each position represents a power of 10.

How do you add binary numbers?

Add column by column from right to left, just like decimal. 0+0=0, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).

What happens with negative results in binary subtraction?

If the result is negative, this calculator shows a minus sign before the binary representation of the absolute value.

How is binary related to hexadecimal?

Every 4 binary digits map directly to one hex digit (0–F), because 2⁴ = 16. This makes hex a convenient shorthand for long binary strings in programming.

Can I divide binary numbers?

Yes. The calculator performs integer division and shows the quotient. If the divisor is zero, an error is shown.

Math

↵ to calculate

Binary Calculator - Binary Addition Subtraction Convert

Add, subtract, multiply, and divide binary numbers. Shows binary, decimal, and hex results.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🤖 Computers only understand a secret language of 0s and 1s. This tool helps you turn normal words and numbers into that computer language — or turn it back into normal language!

📌 Direct Answer & Summary

A binary calculator performs arithmetic operations — addition, subtraction, multiplication, and division — directly on binary (base-2) numbers. It accepts numbers made up of only 0s and 1s and returns results in binary, decimal (base-10), and hexadecimal (base-16), making it essential for computer science, digital electronics, and programming tasks.

Binary Number A

Binary Number B

What is Binary Calculator - Binary Addition Subtraction Convert?

How to use it

1️⃣ Enter Binary Number A (only 0s and 1s).
2️⃣ Enter Binary Number B (only 0s and 1s).
3️⃣ Select the operation: Add, Subtract, Multiply, or Divide.
4️⃣ The result is shown in binary, decimal, and hexadecimal. The conversion table below shows both inputs in all three bases.

Formula

Binary arithmetic follows the same rules as decimal but with only two digits. Binary addition: 0+0=0, 0+1=1, 1+1=10 (carry 1). To compute, convert both binary numbers to decimal integers using parseInt(n, 2), perform the operation, then convert back using .toString(2) for binary and .toString(16) for hex.

💡 See it in action — a real example

1101 (13) + 1011 (11) = 11000 (24, 0x18). 1111 (15) − 0110 (6) = 1001 (9, 0x9). 1010 (10) × 0011 (3) = 11110 (30, 0x1E).

❓ Common questions

What is binary arithmetic?: Binary arithmetic is math performed in base 2, where the only digits are 0 and 1. Each digit position represents a power of 2, unlike decimal where each position represents a power of 10.
How do you add binary numbers?: Add column by column from right to left, just like decimal. 0+0=0, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).
What happens with negative results in binary subtraction?: If the result is negative, this calculator shows a minus sign before the binary representation of the absolute value.
How is binary related to hexadecimal?: Every 4 binary digits map directly to one hex digit (0–F), because 2⁴ = 16. This makes hex a convenient shorthand for long binary strings in programming.
Can I divide binary numbers?: Yes. The calculator performs integer division and shows the quotient. If the divisor is zero, an error is shown.

⚡ Related Math Tools & Calculators

Hex Calculator Scientific Notation Calculator Scientific Calculator