# Binary to Decimal Converter Online Tool

Binary Number2

Decimal Number10

Hex Number16

Octal Number8

## About Binary to Decimal Converter Online Tool:

This online binary to decimal converter tool helps you to convert one input binary number (base 2) into a decimal number (base 10).

## Binary Numeral System:

Binary numeral system has 2 digits, include `(0, 1)`. Four binary digits can be represented by 1 hexadecimal digits, and three binary digits can be represented by one octal digits. Binary is the numeral system that most close to electronic circuit hardware.

## Decimal Numeral System:

Decimal numeral system (also called Hindu-Arabic, or Arabic) has 10 digits, include `(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)`, it's the most used number system in our daily life. Decimal numeral system is also one of the most ancient number system, it's inspired by 10 fingers of human. ## How to convert from binary to decimal?

For binary number represents as below (with n digits):

dn-1dn-2...d2d1d0

For each digit in binary numeral system (base 2), equals to each digit multiply by its position power to 2 in decimal numeral system.

Decimal Output = dn-1 × 2n-1 + ... + d1 × 21 + d0 × 20

Example 1: Convert binary number "1101" to decimal number:

Decimal Output = 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20 = 13

Example 2: Convert binary number "0.101" to decimal number:

Decimal Output = 0 × 20 + 1 × 2-1 + 0 × 2-2 + 1 × 2-3 = 0.625

## Binary to Decimal conversion table:

Binary Decimal Binary Decimal
1 1 10101 21
10 2 10110 22
11 3 10111 23
100 4 11000 24
101 5 11001 25
110 6 11010 26
111 7 11011 27
1000 8 11100 28
1001 9 11101 29
1010 10 11110 30
1011 11 11111 31
1100 12 100000 32
1101 13 100001 33
1110 14 100010 34
1111 15 100011 35
10000 16 100100 36
10001 17 100101 37
10010 18 100110 38
10011 19 100111 39
10100 20 101000 40

Wikipedia (Binary): https://en.wikipedia.org/wiki/Binary_number

Wikipedia (Decimal): https://en.wikipedia.org/wiki/Decimal

## Convert Binary to Decimal with Python:

```def binary_to_decimal(binary_str):
decimal_number = int(binary_str, 2)
return decimal_number

binary_input = '1101'
decimal_output = binary_to_decimal(binary_input)
print('decimal result is:{0}'.format(decimal_output))

-------------------
decimal result is:13```

## Convert Binary to Decimal with Java:

```public class NumberConvertManager {
public static int binary_to_decimal(String binary_str) {
return Integer.parseInt(binary_str, 2);
}

public static void main(String[] args) {
String binary_input  = "1101";
int decimal_output = binary_to_decimal(binary_input);
System.out.println("decimal result is:" + decimal_output);
}
}

-------------------
decimal result is:13```