How do I convert Binary to Decimal on this page?

Enter a Binary value in the converter input and the Decimal result is generated automatically with matching pair rules.

Are fractional values supported here?

Yes for numeric bases. You can enter one radix point and fractional digits when the selected format is numeric.

Can I move to other base-pair converters quickly?

Yes. Related pair links are listed below the converter for fast switching.

Binary to Decimal Converter

developer · number system

Convert Binary to Decimal with a fixed input and output format, step-by-step formulas under the result, and reference tables. Parsing matches the main hub (0b, 0x, leading 0 for octal; one optional . for fractional digits on numeric bases; single character for character mode).

Calculator

Input (Binary)

From: Binary

Result (Decimal)

To: Decimal

Formulas

Enter a value → place-value expansion + division chain.

About Binary

Binary (base 2) uses digits 0 and 1. This tool accepts an optional 0b prefix. You may use one radix point; digits after it use negative powers of two (½, ¼, …). It is the native representation for digital logic and bitwise operations.

About Decimal

Decimal (base 10) uses digits 0–9; no prefix is required. A single . may separate the fractional part (10⁻¹, 10⁻², …). Values are parsed to a number and re-encoded into the target format; very long fractions are limited by floating-point precision.

How to convert binary to decimal

Three steps: symbols → the right math move for this pair → worked examples you can copy on paper. Numeric bases (binary, octal, decimal, hex) also support one radix point and digits after it; character mode stays a single code unit.

Step 1 — Identify the symbols

Input (Binary): Each position is either 0 or 1.

Output (Decimal): Ordinary digits 0–9; each position is a power of ten.

Dev note

Many tools allow a 0b prefix (e.g. 0b1010).

Step 2 — Binary Place Weights

Number positions from the right, starting at 0. At each position, multiply that digit by 2 raised to the position index, then add every term. The total is your decimal number.

Digits after the dot: use negative powers of 2 (2⁻¹, 2⁻², …). Each place is still (digit × weight); add the fractional side to the whole side.

Step 3 — Worked examples

Two practice values in Binary, converted to Decimal using the same rules as Step 2. Example 3 uses a fractional part (digits after the radix point); the hub and pair calculators accept a single . on binary, octal, decimal, and hex inputs.

Example 1

"1010" (Binary) → Decimal.

Toward decimal

Binary "1010"
= 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 2
= 10  (decimal)

Verify: "1010" → 10

Example 2

"1111" (Binary) → Decimal.

Toward decimal

Binary "1111"
= 1×2³ + 1×2² + 1×2¹ + 1×2⁰
= 8 + 4 + 2 + 1
= 15  (decimal)

Verify: "1111" → 15

Example 3

"1010.101" (Binary) → Decimal.

Toward decimal

Binary "1010.101"
Left of . : 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10
Right of .: 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0.125
= 10.625  (decimal)

Verify: "1010.101" → 10.625

Summary

To convert Binary to Decimal, the tool first parses your input strictly as binary, producing a decimal value. For binary, octal, decimal, and hex, you may include one radix point and fractional digits; character input remains a single code unit with no dot. That value is formatted as decimal using the same rules as the main Number System Converter (prefixes 0b, 0, 0x where applicable; character output uses symbolic names for common controls and requires a whole-number code point). Long fractional expansions are truncated to a fixed digit cap; ordinary floating-point rounding may appear in extreme cases.

Relationship context

Binary, Decimal, and the other numeric bases on this site all describe the same numeric value; only the radix changes (including optional fractional digits after one dot). Moving between them is equivalent to changing how the value is written, not to scaling or unit conversion. Binary, octal, and hex align with bit boundaries (powers of two), while decimal is optimized for human arithmetic.

Conversion tables

Binary (input)	Decimal (output)
0	0
0b1	1
0b10	2
0b11	3
0b100	4
0b101	5
0b110	6
0b111	7
0b1000	8
0b1001	9
0b1010	10
0b1111	15
0b10000	16

Binary (input)	Decimal (output)
0b1011	11
0b100000	32
0b1000000	64
0b10000000	128
0b100000000	256
0b1000000000	512
0b10000000000	1024
0b100000000000	2048
0b1000000000000	4096
0b10000000000000	8192
0b100000000000000	16384
0b1000000000000000	32768
0b1111111111111111	65535

More number system pairs

Other fixed input/output converters use the same parsing rules as the hub. Open any pair for the same calculator layout and reference tables.

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