Binary to Decimal Converter

Tired of 1s and 0s? Our Binary to Decimal converter translates computer language into normal numbers. Get your human-readable answer instantly.

Online Binary to Decimal Converter

The free online Binary to Decimal Converter translates base-2 computer language (1s and 0s) into the standard base-10 numbers used in daily life. Computers, routers, and microcontrollers process data entirely using binary switches. However, reading raw strings of bits can be difficult during programming, debugging, or network setup.

This utility removes the need for manual mathematical equations, giving you human-readable decimal integers instantly.

How to Use the Binary to Decimal Converter

This system handles single numbers, grouped bytes, and bulk text files efficiently. Follow these steps to convert your data:

1. Enter Your Binary Data: Type or paste your binary string into the Enter Binary Number box. You can enter simple strings (like 1101) or space-separated bytes (like 0100 0001).
2. Upload a File (Optional): If you have a large dataset saved on your computer, click Upload .txt File to import and process the document automatically.
3. Convert: Click the Convert To Decimal button to process the numbers instantly.
4. Save the Output: The results will appear in the Decimal Output text area. Click Copy To Clipboard to copy the results instantly, or click Download .txt to save the clean decimal conversions into a new file.
5. Reset: Click Clear Text to wipe both fields and start fresh.

How Binary to Decimal Conversion Works

The decimal system is a base-10 system based on positions of tens (1, 10, 100, 1000). Binary is a base-2 system where every position from right to left represents an escalating power of 2 (1, 2, 4, 8, 16, 32, 64, 128, and so on).

To find the decimal equivalent of a binary number, add up the positional values of all the slots that contain a 1.

Conversion Example:

Let’s decode the binary number 1011:

• First digit from the right is in the 1s place (2^0): It is a 1, which gives 1
• Second digit from the right is in the 2s place (2^1): It is a 1, which gives 2
• Third digit from the right is in the 4s place (2^2): It is a 0, which gives 0
• Fourth digit from the right is in the 8s place (2^3): It is a 1, which gives 8

Add the active values together: 8 + 0 + 2 + 1 = 11

If you are dealing with binary strings that represent English letters or full paragraphs instead of standalone numbers, a binary to text converter will translate the bits back into regular words. Conversely, to turn sentences back into binary code, a text to binary converter does the work instantly.

For low-level computing and system debugging, engineers often switch back and forth between binary and base-16 structures. In those cases, using a hex to binary converter helps map out memory addresses and hex flags cleanly.

Binary to Decimal Reference Table

This table illustrates how common 8-bit binary configurations (bytes) translate into human-readable numbers:

Binary Input (Base-2)	Positional Math Breakdown	Decimal Output (Base-10)
00000101	4 + 1	5
00001010	8 + 2	10
00111111	32 + 16 + 8 + 4 + 2 + 1	63
10000000	128	128
11111111	128 + 64 + 32 + 16 + 8 + 4 + 2 + 1	255

Binary, Decimal, and Hexadecimal Conversion Table

This reference table shows the direct relationship between binary numbers, their decimal equivalents, and their corresponding hexadecimal values from 0 through 15.

Binary Number	Decimal Number	Hex Number
0	0	0
1	1	1
10	2	2
11	3	3
100	4	4
101	5	5
110	6	6
111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

Frequently Asked Questions