To convert Binary to Decimal, input binary value in the box below, and then click on the big blue button that says “BINARY to DECIMAL” and your output is generated, copy it or you can download output file.
In Binary number system there are only two digits that are 0 and 1. In this number system every number (value) represents with 0 and. The base of binary number system is 2, because it has only two digits.
Example: What is (110)_{2} in base 10?
(110)_{2} = (1 x 2^{2}) + (1 x 2^{1}) + (0 x 1^{0}) = 6_{10}
In decimal number system there only ten (10) digits from 0 to 9. Every number (value) in this decimal system represents with 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base of this number system is 10, because it has only 10 digits.
Example: 8062 in decimal (base 10)
8062_{10} = (8 x 10^{3}) + (0 x 10^{2}) + (6 x 10^{1}) + (2 x 10^{0})
The method of conversion of binary numbers to decimal number is really simple. Here we have to keep in mind that each of the binary number system is a positional number system, i.e., each of the digits in the number systems discussed above has a positional weight as in the case of the decimal system. We will try to show the process with the help of examples.
Example 1: Convert (10110)_{2 }into a decimal number.
Solution.
The binary number given is 1 0 1 1 0
Positional weights 4 3 2 1 0
Hence the decimal equivalent number is given as:
1 × 2^{4 }+ 0 × 2^{3 }+ 1 × 2^{2 }+ 1 × 2^{1 }+ 0 × 2^{0}
= 16 + 0 + 4 + 2 + 0
= (22)_{10}.
Hence we find that here, for the sake of conversion, we have to multiply each bit with its positional weights depending on the base of the number system.
Decimal |
Binary |
0 |
0 |
1 |
1 |
2 |
10 |
3 |
11 |
4 |
100 |
5 |
101 |
6 |
110 |
7 |
111 |
8 |
1000 |
9 |
1001 |
10 |
1010 |
11 |
1011 |
12 |
1100 |
13 |
1101 |
14 |
1110 |
15 |
1111 |
Decimal Number System is really beneficial in our day to day life while you have to deal with money, height, weight or something else like that. A whole number cannot always give a precise value for such thing and because of it Decimal Number System comes into play. For example, when we measure our weight on a weighing machine, most certainly it won’t show your weight in a whole number so to get an accurate result we use decimals.