# Binary to Decimal converter

In order to use this new binary to decimal converter tool, type any binary value like 1010 into the first field below, and then hit the Convert button. You can see the result in the right field below. It is possible to convert up to 63 binary characters to decimal.

## Binary to decimal converter

Enter binary value like 1010 and press the Convert button:

 Enter binary number: 2 Decimal number: 10 Decimal from signed 8/16/32 bit: 10 Hex number: 16

Decimal to Binary converter ►

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

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

### Binary System

Binary is the simplest kind of number system that uses only two digits of 0 and 1. By using these digits computational problems can be solved by machines because in digital electronics a transistor is used in two states. Those two states can be represented by 0 and 1. That is why this number system is the most preferred in modern computer engineer, networking and communication specialists, and other professionals.

### Decimal System

Decimal number system is the most commonly used and the most familiar one to the general public. It is also known as Base 10 numbering system since it is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has its own position as well as the decimal point. I.e. the number 356.74 has 4 in the Hundredths position, 7 in the Tenths position, 6 in the Units position, 5 in the Tens position, and 3 in the Hundreds position. Decimal number system is also one of the oldest known numeral system, which is historically related to Hindu-Arabic numeral system.

Binary Decimal
0 0
1 1
10 2
11 3
100 4
101 5
110 6
111 7
1000 8
1001 9
1010 10
1011 11
1100 12
1101 13
1110 14
1111 15
10000 16
10001 17
10010 18
10011 19
10100 20
10101 21
10110 22
10111 23
11000 24
11001 25
11010 26
11011 27
11100 28
11101 29
11110 30
11111 31
100000 32
1000000 64
10000000 128
100000000 256