Skip to content
Devtoolry
Sign InJoin for Free

Binary to Decimal Converter

Convert binary to decimal online with the working shown step by step. Handles fractions such as 101.101, signed two's complement values and whole lists at once.

Runs in your browser · Nothing uploaded · No sign-up

Something not working, or missing a feature? Send feedback

About the Binary to Decimal Converter

The Binary to Decimal Converter turns base-2 numbers into ordinary decimal numbers and shows the working: each bit is multiplied by its power of 2 and the results are added. It also reads binary fractions such as 101.101 and signed two's complement values, so it is useful for homework, exam practice and reading register dumps.

Conversion happens in your browser, so your files and records stay private.

How to use the Binary to Decimal Converter

  1. Type a binary number such as 101101, or paste several, one per line.
  2. Turn on "Signed (two's complement)" if the bits are a signed integer, such as 11111111 for -1.
  3. Read the decimal result and the table that multiplies each bit by its power of 2.
  4. Copy one result, or all of them for a pasted list.

Powers of 2

The place value of each bit, counted from the right starting at 0.

Bit positionPowerDecimal value
02^01
12^12
22^24
32^38
42^416
52^532
62^664
72^7128
82^8256
102^101,024
152^1532,768
162^1665,536
312^312,147,483,648
322^324,294,967,296
632^639,223,372,036,854,775,808

Examples

A whole number

Input

101101

Result

45

1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1 = 45.

A binary fraction

Input

101.101

Result

5.625

The bits after the point are worth 0.5, 0.25 and 0.125.

A signed byte

Input

11111111 (Signed on)

Result

-1

Unsigned it is 255; in two's complement 255 − 2⁸ = −1.

Common mistakes

  • Dropping leading zeros of signed values. Two's complement depends on the width. 1111 read as 4 bits is −1, but as 8 bits (00001111) it is 15. Type all the bits of the register or byte.
  • Reading the bits from the wrong end. The rightmost bit is worth 1 and the values double to the left. Starting at the left gives a different, wrong number.

Works well with the Binary to Decimal Converter

Frequently asked questions

How do you convert binary to decimal by hand?

Write the powers of 2 under the bits, starting with 2⁰ = 1 at the right. Add the powers where the bit is 1. For 101101 that is 32 + 8 + 4 + 1 = 45.

How are binary fractions converted?

Bits after the point have negative powers: ½, ¼, ⅛ and so on. 101.101 is 4 + 1 + 0.5 + 0.125 = 5.625. Binary fractions always have an exact decimal value, so nothing is rounded.

What does signed mean here?

Signed numbers use two's complement: the leftmost bit counts as a negative power. In 8 bits, 11111111 is 255 unsigned but -1 signed. The width is the number of bits you type, so add leading zeros (01111111) when the top bit should be 0.

Is there a size limit?

No practical one. The converter uses arbitrary-precision integers, so a 128-bit or 1,000-bit value is converted exactly.

Related tools