Binary to Decimal Converter | Convert Binary to Decimal Numbers

Free online binary to decimal converter. Convert binary numbers to decimal format with step-by-step explanations. Includes conversion table and practice examples.

Binary to Decimal Converter

Input

FromTextBinaryHexadecimalDecimalOctal

ToTextBinaryHexadecimalDecimalOctal

Character EncodingUTF-8ASCIIUTF-16

Convert

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Common Examples

Binary: 1010

Decimal: 10

Powers: 8 + 0 + 2 + 0 = 10

Binary: 1111

Decimal: 15

Maximum 4-bit value

Binary: 10000

Decimal: 16

Power of 2 (2⁴)

Binary: 11111111

Decimal: 255

Maximum 8-bit value (byte)

Understanding Place Values

27	26	25	24	23	22	21	20
128	64	32	16	8	4	2	1

Example: 1101₂

1 × 2³ = 1 × 8 = 8

1 × 2² = 1 × 4 = 4

0 × 2¹ = 0 × 2 = 0

1 × 2⁰ = 1 × 1 = 1

Sum: 8 + 4 + 0 + 1 = 13

How Binary to Decimal Conversion Works

Step-by-Step Process

1. Identify each digit's place value (powers of 2)
2. Multiply each binary digit (0 or 1) by its place value
3. Sum all the results to get the decimal number

Easy Method: Right to Left

1. 1. Start from rightmost digit
2. 2. Multiply by increasing powers of 2
3. 3. Add results as you go

Quick Tips

• Each position doubles in value
• Powers of 2 are easy to spot
• 8-bit numbers max at 255

Common Bit Patterns

10000000

= 128

Leftmost bit (MSB)

11111111

= 255

All bits set (byte)

10101010

= 170

Alternating pattern

01111111

= 127

Max 7-bit value

Related Conversions

Binary to Hex

Binary to Octal

Decimal to Binary

Decimal to Hex