Binary is a base-2 number system using digits 0 and 1, commonly used in computing.

How do I convert binary to decimal?

Multiply each binary digit by 2 raised to the power of its position (from right starting at 0) and sum the results.

Is there an automatic way to convert large binary numbers?

Yes — use this converter to instantly convert long binary strings to decimal without manual calculation.

Binary Converter

Seamlessly translate between Binary (0s and 1s) and Decimal numbers.

Enter Binary Number

Invalid digits! Only 0 and 1 allowed.

Decimal Result

Powers of 2 Reference

Power	Value	Binary
2⁰	1	1
2¹	2	10
2²	4	100
2³	8	1000
2⁴	16	10000
2⁵	32	100000
2⁶	64	1000000
2⁷	128	10000000

Frequently Asked Questions

How to convert Binary to Decimal manually?

Take each digit from the right (starting at position 0) and multiply it by 2 raised to that power. Add all the results together.
Example (101): (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 4 + 0 + 1 = 5.

Why do computers use Binary?

Computers operate using transistors which have two physical states: On (1) and Off (0). Binary is the most efficient way to represent this hardware reality mathematically.