Binary To Decimal

The Binary to Decimal Converter translates binary numbers (base-2) into their decimal (base-10) equivalents. Paste binary digits — 0s and 1s, with or without spaces — click Convert to Decimal, and the tool calculates the result instantly. File upload is also supported.

Binary is the native number system of computers; decimal is the number system humans use every day. Converting between them is a fundamental operation in computer science, networking, embedded development, and digital electronics. The converter handles this calculation automatically — no manual positional arithmetic required.

How to use the Binary to Decimal Converter

1. Paste your binary number into the input field. Use only the characters 0 and 1. Spaces between groups are optional and accepted.

2. Click Convert to Decimal.

3. The decimal equivalent is displayed. Copy it for use in your code, documentation, or calculations.

Worked example: binary 11011010 = decimal 218. Reading from right to left: bit 1 (value 1) = 0 → 0, bit 2 (value 2) = 1 → 2, bit 3 (value 4) = 0 → 0, bit 4 (value 8) = 1 → 8, bit 5 (value 16) = 1 → 16, bit 6 (value 32) = 0 → 0, bit 7 (value 64) = 1 → 64, bit 8 (value 128) = 1 → 128. Sum: 128 + 64 + 16 + 8 + 2 = 218.

How binary to decimal conversion works

The positional weight system

Both binary (base-2) and decimal (base-10) are positional number systems — the value of each digit depends on its position. In decimal, positions are powers of 10 (ones, tens, hundreds, thousands). In binary, positions are powers of 2.

Reading from right to left, each bit position corresponds to the next power of 2:

The conversion calculation

To convert binary to decimal: for each bit that is 1, add the positional weight of that bit. For each bit that is 0, add nothing. The sum is the decimal value. This is why 11111111 in binary equals 255 in decimal — it is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, the sum of all eight positional weights.

Step-by-step worked example — converting 11011010

The maximum value representable by n binary bits: 1 bit = max 1 (2¹ − 1). 4 bits = max 15 (2⁴ − 1). 8 bits = max 255 (2⁸ − 1). 16 bits = max 65,535 (2¹⁶ − 1). 32 bits = max 4,294,967,295 (2³² − 1). 64 bits = max 18,446,744,073,709,551,615 (2⁶⁴ − 1). These are the maximum values of unsigned integers in systems that use 8, 16, 32, or 64-bit integers — for example, 255 is the maximum value in an 8-bit byte, which is why pixel colour channels in RGB images range from 0 to 255.

Common binary values — decimal and hex reference

The table below lists frequently encountered binary values with their decimal and hex equivalents, and their significance in computing contexts:

Unsigned vs signed binary — the two's complement note

This converter treats binary input as unsigned — a positive integer with no sign bit. For unsigned 8-bit binary, the range is 0 (00000000) to 255 (11111111). This is correct for most uses: byte values, colour channels, memory addresses, bitmasks, and most unsigned integer representations.

Two's complement is the standard way computers represent signed integers (both positive and negative). In two's complement 8-bit representation, the most significant bit (leftmost) is the sign bit: 0 means positive, 1 means negative. The value 10000000 in unsigned binary is 128; in two's complement 8-bit, it is −128. If you are working with signed integer data (where negative values are possible), interpret the unsigned decimal result from this converter with the two's complement rule: if the leading bit is 1, the actual signed value is the unsigned decimal minus 2ⁿ (where n is the number of bits).

Usage limits

Related tools

• Decimal to Binary — the reverse: convert a decimal (base-10) number to binary. Enter a decimal integer and get the binary representation.

• Binary to Hex — convert binary to hexadecimal. Hex is the compact notation for binary, with each hex digit representing 4 binary bits.

• Hex to Binary — expand hexadecimal back to binary. One hex digit → 4 binary bits.

• Binary to ASCII — decode 8-bit binary to ASCII text characters. Each byte (8 bits) represents one ASCII character.

Frequently asked questions

How do you convert binary to decimal?

Assign a positional weight to each bit, starting from the rightmost bit (bit 1) with weight 1, and doubling the weight with each position to the left: 1, 2, 4, 8, 16, 32, 64, 128, 256... For each bit that is 1, add that position's weight. For each bit that is 0, add nothing. Sum all the contributions. Example: 1010 = (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1) = 8 + 0 + 2 + 0 = 10.

What is the decimal value of 11111111?

11111111 in binary equals 255 in decimal. It is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the maximum value of an 8-bit byte (2⁸ − 1 = 255) and the maximum value in each RGB colour channel — the reason colours range from 0 to 255.

What is the decimal value of 10000000?

10000000 in binary equals 128 in decimal. It has only one bit set — bit 7 (the leftmost in an 8-bit byte), which has positional weight 2⁷ = 128. This value appears frequently: as the /25 subnet mask last octet (255.255.255.128), as the byte value above which UTF-8 uses multi-byte sequences, and as the sign bit in 8-bit two's complement representation.

What does it mean when a binary number has a leading 1?

In unsigned binary (which this converter uses), a leading 1 simply means the highest positional weight is included. 10000000 = 128 unsigned. In signed two's complement representation, a leading 1 indicates a negative number — 10000000 is −128 in 8-bit two's complement. If you are working with signed integers and the leading bit is 1, the two's complement signed value is the unsigned result minus 2ⁿ, where n is the total number of bits.

Can I convert binary fractions (numbers with a decimal point)?

This converter handles whole binary numbers (integers). Binary fractions (like 0.101) use negative powers of 2 after the binary point: the first position after the point is 2⁻¹ = 0.5, the second is 2⁻² = 0.25, and so on. 0.101 in binary = 0.5 + 0 + 0.125 = 0.625 in decimal. For binary fraction conversion, a dedicated floating-point converter is needed.

What is the maximum decimal value for different bit lengths?

The maximum unsigned decimal value for n bits is 2ⁿ − 1: 4 bits = 15. 8 bits = 255. 16 bits = 65,535. 32 bits = 4,294,967,295. 64 bits = 18,446,744,073,709,551,615. These correspond to the maximum values of uint8_t, uint16_t, uint32_t, and uint64_t in C/C++ and equivalent types in other languages. The pattern is straightforward: add one more bit and the maximum value roughly doubles.

What is the relationship between binary, decimal, and hexadecimal?

All three are representations of the same numeric value in different bases. Binary (base-2) uses digits 0–1; decimal (base-10) uses digits 0–9; hexadecimal (base-16) uses digits 0–9 and A–F. The decimal value 255 is 11111111 in binary and FF in hex. The conversion relationships are: each hex digit = 4 binary bits. Binary is what computers process; decimal is what humans read; hex is the programmer's compact notation for binary data.

Is the Binary to Decimal Converter free?

Yes. The converter is free within the usage limits. Guest users can convert up to 200 words per conversion and run 25 conversions per day. Registering a free ToolsPiNG account increases the word limit to 1,000 words per conversion and the daily limit to 100 conversions.