Binary to Decimal Converter

In order to use this new binary to decimal converter tool, type any binary value like 1010 into the left 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 conversion result in base numbers

Binary System

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1.

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2⁰. In the binary system, each binary digit refers to 1 bit.

Decimal System

The decimal numeral system is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the decimal numeral system has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the n^th power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

The digit 5 is in the position of ones (10⁰, which equals 1),
4 is in the position of tens (10¹)
3 is in the position of hundreds (10²)
2 is in the position of thousands (10³)
Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10^-1) and 7 is in the hundredths (1/100, which is 10^-2) position
Thus, the number 2345.67 can also be represented as follows: (2 * 10³) + (3 * 10²) + (4 * 10¹) + (5 * 10⁰) + (6 * 10^-1) + (7 * 10^-2)

How to Read a Binary Number

In order to convert binary to decimal, basic knowledge on how to read a binary number might help. As mentioned above, in the positional system of binary, each bit (binary digit) is a power of 2. This means that every binary number could be represented as powers of 2, with the rightmost one being in the position of 2⁰.

Example: The binary number (1010)₂ can also be written as follows: (1 * 2³) + (0 * 2²) + (1 * 2¹) + (0 * 2⁰)

How to Convert Binary to Decimal

There are two methods to apply a binary to decimal conversion. The first one uses positional representation of the binary, which is described above. The second method is called double dabble and is used for converting longer binary strings faster. It doesn’t use the positions.

Method 1: Using Positions

Step 1: Write down the binary number.

Step 2: Starting with the least significant digit (LSB - the rightmost one), multiply the digit by the value of the position. Continue doing this until you reach the most significant digit (MSB - the leftmost one).

Step 3: Add the results and you will get the decimal equivalent of the given binary number.

Now, let's apply these steps to, for example, the binary number above, which is (1010)₂

Step 1: Write down (1010)₂ and determine the positions, namely the powers of 2 that the digit belongs to.
Step 2: Represent the number in terms of its positions. (1 * 2³) + (0 * 2²) + (1 * 2¹) + (0 * 2⁰)
Step 3: (1 * 8) + (0 * 4) + (1 * 2) + (0 * 1) = 8 + 0 + 2 + 0 = 10
Therefore, (1010)₂ = (10)₁₀

(Note that the digits 0 in the binary produced zero values in the decimal as well.)

Method 2: Double Dabble

Also called doubling, this method is actually an algorithm that can be applied to convert from any given base to decimal. Double dabble helps converting longer binary strings in your head and the only thing to remember is ‘double the total and add the next digit’.

Step 1: Write down the binary number. Starting from the left, you will be doubling the previous total and adding the current digit. In the first step the previous total is always 0 because you are just starting. Therefore, double the total (0 * 2 = 0) and add the leftmost digit.
Step 2: Double the total and add the next leftmost digit.
Step 3: Double the total and add the next leftmost digit. Repeat this until you run out of digits.
Step 4: The result you get after adding the last digit to the previous doubled total is the decimal equivalent.

Now, let’s apply the double dabble method to same the binary number, (1010)₂

Your previous total 0. Your leftmost digit is 1. Double the total and add the leftmost digit
(0 * 2) + 1 = 1
Step 2: Double the previous total and add the next leftmost digit.
(1 * 2) + 0 = 2
Step 3: Double the previous total and add the next leftmost digit.
(2 * 2) + 1 = 5
Step 4: Double the previous total and add the next leftmost digit.
(5 * 2) + 0 = 10

This is where you run out of digits in this example. Therefore, (1010)₂ = (10)₁₀

Binary to decimal conversion examples

Example 1: (1110010)₂ = (114)₁₀

Method 1:
(0 * 2⁰) + (1 * 2¹) + (0 * 2²) + (0 * 2³) + (1 * 2⁴) + (1 * 2⁵) + (1 * 2⁶)
= (0 * 1) + (1 * 2) + (0 * 4) + (0 * 8) + (1 * 16) + (1 * 32) + (1 * 64)
= 0 + 2 + 0 + 0 + 16 + 32 + 64 = 114

Method 2:
0 (previous sum at starting point)
(0 + 1) * 2 = 2
2 + 1 = 3
3 * 2 =6
6 + 1 =7
7 * 2 = 14
14 + 0 =14
14 * 2 = 28
28 + 0 =28
28 * 2 = 56
56 + 1 = 57
57 * 2 = 114

Example 2: (11011)₂ = (27)₁₀

Method 1:
(0 * 2⁰) + (1 * 2¹) + (0 * 2²) + (1 * 2³) + (1 * 2⁴)
= (1 * 1) + (1 * 2) + (0 * 4) + (1 * 8) + (1 * 16)
= 1 + 2 + 0 + 8 + 16 = 27

Method 2:
(0 * 2) + 1 = 1
(1 * 2) + 1 = 3
(3 * 2) + 0 = 6
(6 * 2) + 1 = 13
(13 * 2) + 1 = 27

Related converters:
Decimal To Binary Converter

Binary Decimal Conversion Chart Table

Binary	Decimal
00000001	1
00000010	2
00000011	3
00000100	4
00000101	5
00000110	6
00000111	7
00001000	8
00001001	9
00001010	10
00001011	11
00001100	12
00001101	13
00001110	14
00001111	15
00010000	16
00010001	17
00010010	18
00010011	19
00010100	20
00010101	21
00010110	22
00010111	23
00011000	24
00011001	25
00011010	26
00011011	27
00011100	28
00011101	29
00011110	30
00011111	31
00100000	32
00100001	33
00100010	34
00100011	35
00100100	36
00100101	37
00100110	38
00100111	39
00101000	40
00101001	41
00101010	42
00101011	43
00101100	44
00101101	45
00101110	46
00101111	47
00110000	48
00110001	49
00110010	50
00110011	51
00110100	52
00110101	53
00110110	54
00110111	55
00111000	56
00111001	57
00111010	58
00111011	59
00111100	60
00111101	61
00111110	62
00111111	63
01000000	64

Binary	Decimal
01000001	65
01000010	66
01000011	67
01000100	68
01000101	69
01000110	70
01000111	71
01001000	72
01001001	73
01001010	74
01001011	75
01001100	76
01001101	77
01001110	78
01001111	79
01010000	80
01010001	81
01010010	82
01010011	83
01010100	84
01010101	85
01010110	86
01010111	87
01011000	88
01011001	89
01011010	90
01011011	91
01011100	92
01011101	93
01011110	94
01011111	95
01100000	96
01100001	97
01100010	98
01100011	99
01100100	100
01100101	101
01100110	102
01100111	103
01101000	104
01101001	105
01101010	106
01101011	107
01101100	108
01101101	109
01101110	110
01101111	111
01110000	112
01110001	113
01110010	114
01110011	115
01110100	116
01110101	117
01110110	118
01110111	119
01111000	120
01111001	121
01111010	122
01111011	123
01111100	124
01111101	125
01111110	126
01111111	127
10000000	128

Binary	Decimal
10000001	129
10000010	130
10000011	131
10000100	132
10000101	133
10000110	134
10000111	135
10001000	136
10001001	137
10001010	138
10001011	139
10001100	140
10001101	141
10001110	142
10001111	143
10010000	144
10010001	145
10010010	146
10010011	147
10010100	148
10010101	149
10010110	150
10010111	151
10011000	152
10011001	153
10011010	154
10011011	155
10011100	156
10011101	157
10011110	158
10011111	159
10100000	160
10100001	161
10100010	162
10100011	163
10100100	164
10100101	165
10100110	166
10100111	167
10101000	168
10101001	169
10101010	170
10101011	171
10101100	172
10101101	173
10101110	174
10101111	175
10110000	176
10110001	177
10110010	178
10110011	179
10110100	180
10110101	181
10110110	182
10110111	183
10111000	184
10111001	185
10111010	186
10111011	187
10111100	188
10111101	189
10111110	190
10111111	191
11000000	192

Binary	Decimal
11000001	193
11000010	194
11000011	195
11000100	196
11000101	197
11000110	198
11000111	199
11001000	200
11001001	201
11001010	202
11001011	203
11001100	204
11001101	205
11001110	206
11001111	207
11010000	208
11010001	209
11010010	210
11010011	211
11010100	212
11010101	213
11010110	214
11010111	215
11011000	216
11011001	217
11011010	218
11011011	219
11011100	220
11011101	221
11011110	222
11011111	223
11100000	224
11100001	225
11100010	226
11100011	227
11100100	228
11100101	229
11100110	230
11100111	231
11101000	232
11101001	233
11101010	234
11101011	235
11101100	236
11101101	237
11101110	238
11101111	239
11110000	240
11110001	241
11110010	242
11110011	243
11110100	244
11110101	245
11110110	246
11110111	247
11111000	248
11111001	249
11111010	250
11111011	251
11111100	252
11111101	253
11111110	254
11111111	255