Convert Binary to Decimal!

This Binary to Decimal Converter lets you convert Binary numbers to decimal quickly and easily.

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How to use the Binary to Decimal Converter

Converter features

🔟 Binary Input length:	Up to 25 digits
⚡ Conversion Speed:	Instant!
➡️ Decimal Output:	Display, Copy, Save
🎯 Conversion Accuracy:	100%

Read (or watch) our tutorial on How to Convert Binary to Decimal to learn more about the process of converting binary numbers to decimal.

Try the Decimal to Binary Converter too!

How to Convert Binary to Decimal

So, you need to know how to convert binary to decimal?  All those ones and zeros can be intimidating.  You can find a binary to decimal converter here, or you can learn to convert yourself – no computer required.

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If you thought complicated formulas were necessary for binary to decimal conversion, you can breathe a sigh of relief.  To convert from binary number system to decimal number system, you really only need to know three things.  First, remember that the ones and zeros that make up binary can be thought of as the answer to a yes or no question.  One for “yes”, and zero for “no”.  Next, if you have an understanding of the powers of 2, this will be a breeze.  The last step is basic addition.

The (Super) Powers of 2

We can thank the powers of 2 for making this so easy.  If you’re not familiar with them, having a table for reference will make your job even easier.  You won’t need an extensive table unless you’re converting very large binary numbers.  For example, if the binary number you want to convert is three digits long, you’ll only need the first three powers of 2 (2⁰ , 2¹, and 2²).

Let’s look at a three-digit binary number, 101.

To convert 101 in binary to decimal, we’ll must use the first three powers of 2.  The most straightforward way to visualize this is to write your binary number, and above it, fill in powers of 2. Just remember to start from 2⁰ on the right, and work your way left until you’ve run out of binary digits.

We have 1, 0, and 1, and a power of 2 for each binary digit. We start from the rightmost digit, which is the Least Significant Bit (LSB): look at 2⁰; what’s underneath it?  A one.  This indicates we will use 2⁰ in the decimal output.

Now, let’s work on the next leftmost digit.  What’s under 2¹?  A zero.  This means we will not use 2¹.  And under 2²?  Another one.  To find out what 101 is in decimal, we’ll need 2⁰ and 2².

The rest is simple – 2⁰ and 2² are 1 and 4, respectively.  Now just add 1 + 4. The binary number 101 is the decimal 5.

Just remember to always proceed from right to left, or from the Least Significant Bit (LSB, the rightmost digit) to the Most Significant Bit (MSB, the leftmost digit).

It’s incredibly easy once you can think of 1 as a “yes”, and 0 as a “no”.  Bigger numbers work in the same way.  Let’s throw some extra zeros into the mix and use 100001.  It’s long, but the method is identical.  We just need 6 powers of 2 this time; one for each digit in the binary number.

Which powers of 2 correspond to a one?  Only 2⁶ and 2⁰.  Now we add those powers of 2 together.  100001 as a decimal is 33.

Just to prove how simple converting binary to decimal is, let’s look at an even longer binary figure: 11001100.  We’ll need to go all the way to 2⁷ for this conversion.

All we need to do is add the powers of 2 we used.  Remember, we only “use” them when they correspond to a one.   In this case, we need to add 128, 64, 8, and 4 to find the decimal.  Everything else is indicated by a zero, so we don’t need to include them!  11001100 in binary is the decimal 204.

If you want to try it out for yourself, you can use the binary to decimal calculator on this page to check your work.  Practice a few times, and you’ll be speaking the language of computers with ease.

Table of the First hundred Binary numbers in Decimal

For your convenience, the following table shows the binary numbers from 0 to 1100100 along with their Decimal representation.

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
100001	33
100010	34
100011	35
100100	36
100101	37
100110	38
100111	39
101000	40
101001	41
101010	42
101011	43
101100	44
101101	45
101110	46
101111	47
110000	48
110001	49
110010	50
110011	51
110100	52
110101	53
110110	54
110111	55
111000	56
111001	57
111010	58
111011	59
111100	60
111101	61
111110	62
111111	63
1000000	64
1000001	65
1000010	66
1000011	67
1000100	68
1000101	69
1000110	70
1000111	71
1001000	72
1001001	73
1001010	74
1001011	75
1001100	76
1001101	77
1001110	78
1001111	79
1010000	80
1010001	81
1010010	82
1010011	83
1010100	84
1010101	85
1010110	86
1010111	87
1011000	88
1011001	89
1011010	90
1011011	91
1011100	92
1011101	93
1011110	94
1011111	95
1100000	96
1100001	97
1100010	98
1100011	99
1100100	100

Questions and Answers about Binary to Decimal conversion