Math

Base 2 to Base 10 Converter

Convert Base 2 (Binary) to Base 10 (Decimal)

This is the same conversion as binary to decimal, using the academic textbook phrasing. In base 2, each digit position represents a power of 2. To convert to base 10, multiply each digit by its positional weight and sum.

Number Base Conversion Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

ASCII Letter A

Convert the ASCII code for uppercase A (65) across all bases.

Key values: Decimal 65 · Binary 1000001 · Hex 41

Byte Maximum

The largest value a single byte can hold (255).

Key values: Decimal 255 · Binary 11111111 · Hex FF

Hex Color Code

Convert a common hex color code (deep sky blue) to other bases.

Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles

Documentation

This calculator is also known as Base 2 to Base 10 Converter.

Read the complete guide

The Positional Notation Formula

For a number in base b with digits d_n...d_1 d_0, the decimal value is: N = d_n * b^n + ... + d_1 * b^1 + d_0 * b^0. For base 2: N = d_n * 2^n + ... + d_0 * 2^0.

Examples

Textbook Example

Convert 10110 (base 2) to base 10.

1*16 + 0*8 + 1*4 + 1*2 + 0*1 = 22.

Key takeaway: 10110 in base 2 equals 22 in base 10.

Powers of Two

Convert 10000000 (base 2) to base 10.

1*128 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 128.

Key takeaway: A single 1 followed by N zeros in binary equals 2^N in decimal.

Exam Practice

Convert 1100100 (base 2) to base 10.

64 + 32 + 0 + 0 + 4 + 0 + 0 = 100.

Key takeaway: 1100100 binary = 100 decimal. A handy number to remember!

Study Tips for Base Conversion

Prepare for exams with these tips:

Write out the powers of 2 across the top of your work
Practice both directions: base 2 to 10 and base 10 to 2
Use this calculator to check your homework answers

Frequently Asked Questions about Base 2 to Base 10 Converter

Is "base 2 to base 10" the same as "binary to decimal"?

Yes, they are identical. "Base 2" is the formal mathematical term for binary, and "base 10" is the formal term for decimal.

What is Horner's method for binary-to-decimal conversion?

Horner's method processes digits left to right: start with 0, for each digit multiply by 2 and add the digit. For 1011: ((1*2 + 0)*2 + 1)*2 + 1 = 11. This avoids computing powers of 2.

Why does my textbook use "base" instead of "binary"?

Textbooks use the formal mathematical terminology where "base" (or "radix") refers to the number of unique digits in a numeral system. "Binary" and "base 2" are synonymous, as are "decimal" and "base 10".