What is the positional notation method?

Each binary digit (bit) represents a power of 2 based on its position. The rightmost bit has weight 2⁰ = 1, the next has weight 2¹ = 2, then 2² = 4, and so on. The decimal value is the sum of all weights where the bit is 1.

Does the input need a "0b" prefix?

No prefix is needed. Enter raw binary digits (0s and 1s) only. The converter will flag any character that is not 0 or 1 as invalid.

How large a binary number can I convert?

The converter uses JavaScript's BigInt internally, so it handles arbitrarily large binary strings without precision loss, well beyond the 53-bit limit of regular floating-point numbers.

What is binary 1111 1111 in decimal?

Binary 11111111 (8 ones) equals decimal 255. It is the maximum value of one unsigned byte.

What does binary 0 equal in decimal?

Binary 0 equals decimal 0. A string of all zeros also equals 0.

Can I convert signed (two's complement) binary numbers?

This tool treats all input as unsigned binary integers. For two's complement interpretation you would need to know the intended bit-width and apply the sign bit separately.

Binary to Decimal Converter

Name: Binary to Decimal Converter
Availability: InStock
Author: Nham Vu

Convert any binary number to decimal (base 10) and see the full positional breakdown instantly.

Binary Input

Enter binary number (digits 0 and 1 only)

Quick examples

Decimal Output

Enter a binary number and press Convert

Decimal result

Binary digits

Highest power of 2

Positional breakdown

Position	Bit	Weight (2^n)	Contribution

Sum =

Copied!

Summary

Convert any binary number to decimal (base 10) and see the full positional breakdown instantly.

How it works

Type or paste a binary number into the input field.
Each bit is assigned a positional weight equal to 2 raised to its position index (rightmost = 2⁰).
Bits with value 1 contribute their positional weight; bits with value 0 contribute nothing.
All contributing weights are summed to produce the decimal result.
A step-by-step table shows every bit, its weight, and whether it is included in the sum.

Use cases

Convert binary values from hardware datasheets or microcontroller registers to decimal.
Verify manual binary-to-decimal calculations against a trusted reference.
Learn positional notation for computer science or digital electronics courses.
Decode binary-encoded integers found in network packets or file formats.
Cross-check the output of other base-conversion tools.
Help students visualize how binary place values work.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu