Convert Binary to Decimal

Convert binary numbers to decimal with the working shown.

Base 10 value

255

11111111 in base 2

Decimal

255

Binary

11111111

Hexadecimal

Octal

377

Bit length

8 bits

Bytes needed

Each digit × 2 raised to its position from the right, summed.

Place-value expansion.
Digit	Value	Place	Contribution
1	1	2^7	128
1	1	2^6	64
1	1	2^5	32
1	1	2^4	16
1	1	2^3	8
1	1	2^2	4
1	1	2^1	2
1	1	2^0	1

What does Binary to Decimal Converter do?

Convert a binary number to decimal and see the place-value expansion that produced it. Handles arbitrarily long binary strings exactly, which matters when working with 64-bit values.

How to Use Binary to Decimal Converter

1
Enter a binary numberOnly 0 and 1; spaces are ignored.
2
Read the decimal valueShown with the working underneath.
3
Copy itOne tap.

Key Features

Place-value expansion showing how the total is built
Exact for values of any length via BigInt arithmetic
Hexadecimal and octal shown alongside
Bit count reported
Rejects non-binary digits with a clear message

Frequently Asked Questions

How do I convert binary to decimal by hand?

Give each digit a place value doubling from the right — 1, 2, 4, 8, 16 — then add the values where the digit is 1. 10110 is 16 + 4 + 2 = 22.

What is the largest value in 8 bits?

11111111, which is 255. In general n bits hold values from 0 to 2ⁿ − 1, so 16 bits reach 65,535 and 32 bits reach about 4.29 billion.

How do I handle negative binary numbers?

Computers use two’s complement, where the leading bit indicates sign at a fixed width. In 8-bit two’s complement, 11111111 is −1 rather than 255. This converter treats input as unsigned unless you add a minus sign.