Binary Calculator

Add, subtract, multiply and divide binary numbers and see the answer in binary, decimal, hex and octal. Example: 1011 + 110 = 10001, which is 11 + 6 = 17.

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First number

Operation

Second number

How to use the Binary Calculator

Type the first number using only valid binary digits (0 and 1).
Choose an operation and type the second number.
Press Calculate to see the answer in binary, decimal, hex and octal.

Formula and method

Binary is base 2: each place is a power of 2 (1, 2, 4, 8, 16…). 1011 = 8 + 2 + 1 = 11. The calculator converts to decimal, applies the operation and converts back.

Worked example: 1011 + 110

Step	Result
1011 in decimal	11
110 in decimal	6
Sum	17
17 in binary	10001

Binary place values

Place	Value
2^7	128
2^6	64
2^5	32
2^4	16
2^3	8
2^2	4
2^1	2
2^0	1

Binary addition rules

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 (write 0, carry 1). Work from the right just as in decimal addition.

Frequently asked questions

How do I add binary numbers?

Add column by column from the right, carrying 1 when 1 + 1 = 10.

How do I convert binary to decimal?

Add the place values (powers of 2) of every digit that is 1.

What is 1010 in decimal?

10.

How do I multiply binary numbers?

Like decimal long multiplication, but each partial product is either 0 or the number shifted.

Can the calculator handle large numbers?

Yes, it uses arbitrary-size integers.

What are negative binary numbers?

Use a minus sign here; computers often use two’s complement.

Sources

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Effortless Math Team

22 minutes ago