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 nth 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 |
Recent Comments
jacques redding 2024-07-30 13:03:57
Hi is there any one that can help with the following, to convert binary data in wiegand bits: 10000000 00000000 10110000 00010110 10001111
11011010.
48bit hid mifare m1l card.
BimBimBamBam 2024-06-08 17:31:36
@Fatima 100 in dozenal (duodecimal) is 144 in decimal
BimBimBamBam 2024-06-08 17:30:50
@Taani 01000000 is 64 in decimal
Joe Kraft 2024-04-15 18:01:32
I really appreciate the binary table, it's hard to find one that is actually in a normal format and useful!!
Emmie 2024-03-21 03:01:26
@Richard possibly a lot! It'll probably be up to more than 9 0's and 1's
Emmie 2024-03-21 02:57:40
This makes a lot of sense with these calculations! I am 13 years old in 8th Grade standard 6
Richard 2023-11-10 15:38:52
how long does it take to convert 4milion bit binary number decimal
Taani 2022-09-09 06:02:14
How to turn 01000000 into decimal using Double Dabble(method 2)?
sasha 2022-07-06 05:47:16
really good. helps you save time
Bharath CR 2022-06-15 14:40:15
It was use full for me I got more thing to know from this i enjoyed a lot
Rama Rao 2022-03-03 03:41:56
It is so helpful for researchers on Bitcoin
Guest 2022-02-05 09:18:24
@dilantaher 111.0101 = 7.3125
Malshan 2021-11-10 10:13:46
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
Fatima 2021-11-08 01:12:08
17.“Schoolhouse Rock’ had a song called ‘Little Twelvetoes’ which had an alien character with 6 fingers on each hand who could count by 12 as easily as we count by 10. If he counted to 100 in his base 12 (duodecimal), what would that be in decimal?
plz help me
Answer?
Fatima 2021-11-08 01:10:06
Assign a binary code in some orderly manner to the 52 playing cards. Use the minimum number of bits. (4)
plz help me
plz send me solution of this question
Guest 2021-10-21 13:58:30
(73)2=(?)10Ans?
Josip 2021-10-10 13:14:30
Excellent tool. Kudos.
Souvik 2021-10-02 01:44:07
This is a great website and useful
guy 2021-09-29 23:14:09
helps a lot!
Adrita Bandyopadhyay 2021-09-01 15:04:16
Wonderful website for tables and conversion. Thank you for this great help.