⚡ Free Binary Converter

Binary to Decimal Converter

Convert a binary number to decimal instantly with an accurate base-2 to base-10 calculator. Enter any unsigned binary integer made from 0s and 1s to see its decimal value, bit length, place-value calculation, and conversion details.

✓ Free to use ✓ No sign-up ✓ Large-number support ✓ Runs in your browser

Binary → Decimal

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Binary Number Base 2

BIN

Use only the binary digits 0 and 1.

Try:

✓ Decimal Result

Base 10 decimal value

Input bits 0

Significant bits 0

Number system Base 2 → Base 10

Calculation:

What Is a Binary to Decimal Converter?

A binary to decimal converter changes a number written in the binary number system (base 2) into its equivalent value in the decimal number system (base 10). Binary uses only two digits—0 and 1—while the decimal system used in everyday arithmetic uses the digits 0 through 9.

Computers and digital electronics represent information using binary states, so binary values appear frequently in programming, computer architecture, networking, digital logic, embedded systems, and computer science education. Decimal notation is usually easier for people to read, which makes binary-to-decimal conversion useful when interpreting bit patterns and numeric values.

BinaryCon performs the conversion directly in your browser. For integer inputs, the calculator uses arbitrary-size integer arithmetic rather than ordinary floating-point calculations, allowing it to preserve exact values for binary numbers that are much larger than JavaScript’s normal safe-integer range.

Binary system

Binary is a positional base-2 system. Every position represents a power of 2, such as 1, 2, 4, 8, 16, 32, and 64.

Decimal system

Decimal is a positional base-10 system. Each position represents a power of 10 and uses digits from 0 through 9.

How to Convert Binary to Decimal With This Calculator

The converter is designed for quick conversions while still showing enough information to understand the result.

Enter the binary number

Type or paste a value such as 101101. A valid unsigned binary integer contains only 0s and 1s.

Select Convert to Decimal

The calculator interprets your input as a base-2 integer and converts it to its exact base-10 value.

Review the decimal result

You will see the converted decimal number together with the number of entered bits and significant bits.

Check the calculation

For reasonably sized inputs, the result panel also shows the powers of two that contribute to the decimal total.

Copy the result

Use the Copy Result button when you need the decimal value for code, homework, documentation, calculations, or another BinaryCon tool.

Binary to Decimal Formula

Binary is a positional number system. Starting at the rightmost bit, each position has a value equal to a power of 2. The rightmost position is 2⁰, the next is 2¹, then 2², and so on. Multiply each binary digit by its corresponding power of 2 and add the products.

Decimal = b_n×2ⁿ + … + b₂×2² + b₁×2¹ + b₀×2⁰

Each b is a binary digit with a value of either 0 or 1. A position containing 1 contributes its power-of-two value to the total. A position containing 0 contributes nothing.

Place values for a 6-bit number Position: 5 4 3 2 1 0
Power: 32 16 8 4 2 1 This repeating powers-of-two pattern is the foundation of binary-to-decimal conversion.

Worked Example: Convert 101101 Binary to Decimal

Consider the binary number 101101₂. It contains six positions. From left to right, those positions correspond to powers 2⁵ through 2⁰.

Step 1: Expand each binary digit by its place value 101101₂
= 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ Step 2: Evaluate the powers of two = 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1 Step 3: Add the active place values = 32 + 8 + 4 + 1
= 45 Therefore, 101101₂ = 45₁₀.

Notice that the positions containing zero—16 and 2—are not included in the final sum. This makes manual conversion quicker: identify the positions containing 1 and add only their powers of two.

Binary to Decimal Conversion Table

The following reference table shows common unsigned binary values and their decimal equivalents. These values are useful for learning binary place values and checking small conversions manually.

Binary	Decimal	Binary	Decimal
`0`	0	`1000`	8
`1`	1	`1001`	9
`10`	2	`1010`	10
`11`	3	`1011`	11
`100`	4	`1100`	12
`101`	5	`1101`	13
`110`	6	`1110`	14
`111`	7	`1111`	15
`10000`	16	`100000`	32
`11111`	31	`111111`	63
`1000000`	64	`10000000`	128
`11111111`	255	`100000000`	256
`1000000000`	512	`10000000000`	1024

Powers of Two Used in Binary Conversion

Memorizing a few common powers of two can make manual binary conversion much faster. Each time you move one position to the left in a binary number, the place value doubles.

Power	Decimal Value	Power	Decimal Value
2⁰	1	2⁵	32
2¹	2	2⁶	64
2²	4	2⁷	128
2³	8	2⁸	256
2⁴	16	2¹⁰	1024
2¹⁶	65,536	2²⁰	1,048,576

Quick shortcut: a binary value containing a single 1 followed by n zeros equals 2ⁿ. For example, 10000000000₂ has ten zeros, so its decimal value is 2¹⁰ = 1024.

Do Leading Zeros Change a Binary Number?

Leading zeros do not change the numeric value of an unsigned binary integer. For example, 1010, 01010, and 00001010 all represent decimal 10.

The number of written bits can still matter in computing contexts because data is often stored in fixed widths such as 8, 16, 32, or 64 bits. For that reason, BinaryCon reports both the number of digits you entered and the number of significant bits after unnecessary leading zeros are ignored.

Example 00001010₂ = 10₁₀ Entered width: 8 bits
Significant width: 4 bits

Where Binary to Decimal Conversion Is Used

Binary conversion is not limited to classroom exercises. Understanding how a base-2 pattern maps to a decimal quantity is useful throughout computing and digital systems.

Programming

Developers may inspect flags, bit fields, masks, permissions, packed values, or binary literals and need an easier-to-read decimal equivalent.

Digital electronics

Logic circuits and registers work with binary states. Converting an output pattern to decimal can make its numeric meaning easier to interpret.

Computer science education

Place-value conversion helps students understand number systems, positional notation, bits, powers of two, and how computers represent integers.

Networking and systems

Binary representation appears in subnet masks, addresses, permissions, protocol fields, status registers, and other low-level system values.

Common Binary to Decimal Conversion Mistakes

Most manual conversion errors come from incorrect place values rather than difficult arithmetic. These checks can help you avoid them.

Starting with 2¹ instead of 2⁰

The rightmost binary digit always has place value 2⁰ = 1. Starting at 2¹ doubles the final interpretation incorrectly.

Reading a binary value as decimal

Binary 1010 is not decimal one thousand ten. It represents 8 + 2, which equals decimal 10.

Using digits other than 0 and 1

A standard binary numeral cannot contain 2 through 9. This converter identifies such input instead of silently producing a misleading answer.

Ignoring signed-number rules

A fixed-width bit pattern can represent a negative number when interpreted using two’s complement. This particular converter treats your input as an unsigned binary integer.

Unsigned Binary vs Signed Binary

The same visible bit pattern can have different meanings depending on how a computer system interprets it. This calculator performs an unsigned binary-to-decimal conversion, meaning every bit contributes to a non-negative magnitude.

For example, the 8-bit pattern 11111111 equals 255 when interpreted as an unsigned integer. Under 8-bit two’s-complement signed interpretation, however, the same pattern represents -1. The distinction is determined by the chosen representation and bit width, not by the visible characters alone.

Important: If your binary value represents a signed two’s-complement number, do not assume the unsigned result is the intended signed value. Use the appropriate bit width and signed conversion method.

Related BinaryCon Converters

Continue converting the same binary value into other common number systems and representations using these related tools.

Binary to Decimal Converter FAQs

These answers cover common questions about base-2 numbers, decimal conversion, bit width, accuracy, and manual calculation.

What is the easiest way to convert binary to decimal?

For a quick answer, enter the binary value into the converter above. For manual conversion, assign powers of two from right to left, beginning with 2⁰. Add the place values wherever the binary digit is 1. For example, 10110₂ represents 16 + 4 + 2, so the decimal value is 22.

What is 1010 in decimal?

Binary 1010 equals decimal 10. Its place values are 8, 4, 2, and 1. The active positions are 8 and 2, giving 8 + 2 = 10.

What is 1111 binary in decimal?

1111₂ equals 15₁₀. All four positions are active, so the calculation is 8 + 4 + 2 + 1 = 15.

What is 11111111 in decimal?

As an unsigned binary integer, 11111111₂ equals 255. It is the largest value that can be represented by eight unsigned bits because 2⁸ − 1 = 255. If those eight bits are instead interpreted as an 8-bit two’s-complement signed integer, the interpretation would be different.

Can a binary number contain digits other than 0 and 1?

No. Standard base-2 notation uses only the digits 0 and 1. A string such as 10201 is therefore not a valid binary numeral. This calculator validates the input and asks you to remove non-binary digits before performing the conversion.

Does a leading zero change the decimal value?

No, not for an unsigned integer. 101, 0101, and 00000101 all have decimal value 5. Leading zeros may still communicate a fixed storage width, such as an 8-bit value, which can be important in computing contexts.

How do you convert a large binary number to decimal?

Mathematically, the process is the same regardless of length: each position represents a power of two. For long binary numbers, manual expansion becomes inconvenient and ordinary floating-point software can lose integer precision. BinaryCon uses JavaScript BigInt for the unsigned integer calculation, so large inputs can be represented exactly rather than rounded to the nearest floating-point value.

What does base 2 to base 10 mean?

Base 2 is another name for the binary number system because it has two possible digits. Base 10 is the decimal number system because it has ten digits, 0 through 9. Converting base 2 to base 10 means expressing the same numerical quantity using decimal notation.

Why do binary place values use powers of two?

In any positional number system, each position is a power of the system’s base. Decimal positions use powers of 10; hexadecimal positions use powers of 16; binary positions use powers of 2. Therefore binary positions progress as 1, 2, 4, 8, 16, 32, 64, 128, and so forth.

Is binary 100 equal to decimal 100?

No. Binary 100₂ equals decimal 4. Its digits occupy the 4, 2, and 1 positions, and only the 4 position contains a 1. Decimal 100 written in binary is 1100100₂.

Does this converter support binary fractions?

This version is designed for binary integers, so inputs such as 101.101 are not accepted. Binary fractions use negative powers of two to the right of the binary point—for example, 2^-1, 2^-2, and 2^-3—and require a fractional conversion method.

Is the calculator suitable for signed two’s-complement values?

The main result is an unsigned interpretation. Signed two’s-complement conversion requires knowing the intended bit width because the most significant bit participates in the sign interpretation. For example, 11111111 can mean unsigned 255 or signed -1 depending on the representation. Use BinaryCon’s Two’s Complement tool when that interpretation is required.

Is my binary number uploaded or stored?

The conversion logic on this page runs directly in your browser and does not require an external conversion API. You can therefore use the calculator repeatedly without creating an account merely to perform the calculation.

Fast Binary Conversion Whenever You Need It

Keep BinaryCon available for quick number-system conversions, verified reference values, worked examples, and practical binary tools—free to use without creating an account.