Binary-Decimal Converter - Free Number System Converter Tool

DownloadDaisy Header

Conversion Type

Choose the type of conversion you want to perform

Binary to Decimal Decimal to Binary

Enter Number

Enter a binary number (only 0s and 1s)

✓ Result copied to clipboard successfully!

⚠ Please enter a valid number

Result:

Number System Conversion

Binary (Base-2): Uses only digits 0 and 1. Each position represents a power of 2.
Decimal (Base-10): Uses digits 0-9. Our standard counting system.
Binary to Decimal: Multiply each digit by its corresponding power of 2 and sum the results.
Decimal to Binary: Repeatedly divide by 2 and collect remainders in reverse order.

How to Use the Binary to Decimal Converter

To use this free Binary to Decimal Converter:

Enter a binary number (e.g., 1101) into the input box above.
Click the "Convert" button to see its decimal value instantly.
The tool will show the exact base-10 result, including calculation breakdown.

What is a Binary Number?

A binary number is a number expressed in base-2 numeral system. It uses only two digits: 0 and 1. Each digit represents a power of 2.

Example: 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀

What is a Decimal Number?

A decimal number is written in base-10 and uses ten digits: 0 to 9. Each digit counts a power of 10, just like how we normally write numbers in everyday life.

Example: 653₁₀ = 6×10² + 5×10¹ + 3×10⁰ = 653

How to Convert Binary to Decimal Manually

Use the formula below to convert any binary number into decimal:

decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + ... + dₙ×2ⁿ

Where d is the binary digit and n is the position index from right (starting at 0).

Example:

Convert 111001₂ to decimal:

Binary digits:    1   1   1   0   0   1
Power of 2:      2⁵  2⁴  2³  2²  2¹  2⁰

Result: 1×32 + 1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 57₁₀

Binary to Decimal Conversion Table

Binary	Decimal	Hex
0	0	0
1	1	1
10	2	2
11	3	3
100	4	4
101	5	5
110	6	6
111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F
10000	16	10
10100	20	14
11001	25	19
11111	31	1F
100000	32	20
1000000	64	40
10000000	128	80
100000000	256	100

Why Use Our Binary to Decimal Tool?

Instant Conversion: Get real-time results without coding knowledge.
Mobile Friendly: Works on all screen sizes, from desktop to mobile.
Free & Fast: No login, no cost — just pure binary to decimal power.

Binary–Decimal Converter

Conversion Steps: