Math
Binary to Decimal Converter
Type a binary number, with or without a binary point, and get its decimal value along with the place-value table that produces it.
Switch to signed mode to read the same bits as a two's complement number, and see the hex and octal equivalents alongside.
Digits 0 and 1 only. A binary point is allowed (1101.101). Spaces, underscores, or a 0b prefix are fine.
Choose two's complement when the leftmost bit is a sign bit.
Try an example
Result
Converted value
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- Decimal
- —
- Binary
- —
- Hexadecimal
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- Octal
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What the binary to decimal converter solves
Every binary digit stands for a power of two. Reading from the right, the places are worth 1, 2, 4, 8, 16, and so on; places after the binary point are worth 1/2, 1/4, 1/8. To convert, multiply each bit by its place value and add. This converter shows that table for any length of binary number and handles fractions and signed patterns.
Place values of the first eight bits
| Bit position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Weight | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
How to use it
- Enter the binary number. Leading zeros, spaces between nibbles, and a 0b prefix are all accepted.
- Add a binary point for fractional values, for example 0.101.
- Choose Unsigned to read the bits as a plain The length or size of a vector, ignoring which way it points., or Signed two's complement and a bit width to treat the leftmost bit as the sign.
- Read the place-value table: each row is one bit times its weight, and the sum is the decimal answer.
How to read the answer
The main answer is the decimal value. Fractional binary always converts to a terminating decimal (because 2 divides 10), so results like 0.625 are exact. In signed mode, a leading 1 makes the value negative; the steps show the invert-and-add-1 method used to find the magnitude.
Common mistakes and edge cases
- Reading place values from the left. The rightmost bit is the ones place; weights grow toward the left.
- Typing a digit other than 0 or 1. The converter tells you exactly which character is not a binary digit.
- Assuming a leading 1 means negative. It only does in signed mode with a fixed bit width; unsigned 1111 is 15, signed 8-bit 11111111 is −1.
- Fractions after the binary point use negative powers: .1 = 0.5, .01 = 0.25, .001 = 0.125.
Worked examples
Whole binary number
101101
Converted value
45
Binary fraction
1101.101
Converted value
13.625
Zero
0000
Converted value
0
Signed 8-bit pattern
11111011 as two's complement
Converted value
-5
Negative with a sign
−1010
Converted value
-10
Large value
32 ones
Converted value
4,294,967,295
Invalid digit
10201
Converted value
—
Frequently asked questions
How do you convert binary to decimal by hand?+
Write the place values 1, 2, 4, 8, … under the bits from right to left, multiply each bit by its place value, and add the products. 1011 = 8 + 0 + 2 + 1 = 11.
What is 1101 in decimal?+
1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
How do binary fractions convert?+
Bits after the binary point are worth 1/2, 1/4, 1/8, and so on. 0.101 = 0.5 + 0 + 0.125 = 0.625. Every finite binary fraction is an exact finite decimal.
When is a binary number negative?+
Only when you agree to read it as signed. In two's complement at a fixed width, a leading 1 means negative: 8-bit 11111011 is −5, while unsigned it is 251.
Why does the converter also show hex and octal?+
Hex and octal are shorthand for binary (4 bits and 3 bits per digit). Seeing all three helps when reading memory addresses, colors, and file permissions.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026