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Binary to Decimal converter FullScreen

Convert binary numbers to decimal effortlessly with our online tool. Whether you have a binary string or a series of binary digits, our converter can accurately convert it into decimal form. Simply input the binary number and let our converter do the rest. It supports both unsigned and signed binary numbers, providing flexibility for different applications.

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What is Binary to Decimal converter

A Binary to Decimal converter is a tool that allows you to convert binary numbers (base-2) into decimal numbers (base-10). The binary system uses only two digits, 0 and 1, while the decimal system uses ten digits, 0 to 9.

Here's how a Binary to Decimal converter typically works:

  1. Input the binary number you want to convert.
  2. Starting from the rightmost digit, assign each digit a positional value of 2 raised to the power of its position (from right to left), starting from 0.
  3. Multiply each binary digit by its corresponding positional value and sum them up.
  4. The sum obtained is the decimal equivalent of the binary number.

For example:

  • Converting the binary number 1010 to decimal would be calculated as: (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8 + 0 + 2 + 0 = 10.

Binary to Decimal converters are commonly used in computer programming and digital systems analysis. They are available as online tools, calculator applications, or programming language functions for convenient conversion between binary and decimal representations.

How to convert binary to decimal

For binary number with n digits:

dn-1 ... d3 d2 d1 d0

The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):

decimal = d0×20 + d1×21 + d2×22 + ...

Example

Find the decimal value of 1110012:

binary number: 1 1 1 0 0 1
power of 2: 25 24 23 22 21 20

1110012 = 1⋅25+1⋅24+1⋅23+0⋅22+0⋅21+1⋅20 = 5710

Binary to decimal conversion table

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
10000 16 10
10001 17 11
10010 18 12
10011 19 13
10100 20 14
10101 21 15
10110 22 16
10111 23 17
11000 24 18
11001 25 19
11010 26 1A
11011 27 1B
11100 28 1C
11101 29 1D
11110 30 1E
11111 31 1F
100000 32 20
1000000 64 40
10000000 128 80
100000000 256 100

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