# 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.

swap conversion: Decimal To Binary Converter
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

BinaryDecimal
000000011
000000102
000000113
000001004
000001015
000001106
000001117
000010008
000010019
0000101010
0000101111
0000110012
0000110113
0000111014
0000111115
0001000016
0001000117
0001001018
0001001119
0001010020
0001010121
0001011022
0001011123
0001100024
0001100125
0001101026
0001101127
0001110028
0001110129
0001111030
0001111131
0010000032
0010000133
0010001034
0010001135
0010010036
0010010137
0010011038
0010011139
0010100040
0010100141
0010101042
0010101143
0010110044
0010110145
0010111046
0010111147
0011000048
0011000149
0011001050
0011001151
0011010052
0011010153
0011011054
0011011155
0011100056
0011100157
0011101058
0011101159
0011110060
0011110161
0011111062
0011111163
0100000064
BinaryDecimal
0100000165
0100001066
0100001167
0100010068
0100010169
0100011070
0100011171
0100100072
0100100173
0100101074
0100101175
0100110076
0100110177
0100111078
0100111179
0101000080
0101000181
0101001082
0101001183
0101010084
0101010185
0101011086
0101011187
0101100088
0101100189
0101101090
0101101191
0101110092
0101110193
0101111094
0101111195
0110000096
0110000197
0110001098
0110001199
01100100100
01100101101
01100110102
01100111103
01101000104
01101001105
01101010106
01101011107
01101100108
01101101109
01101110110
01101111111
01110000112
01110001113
01110010114
01110011115
01110100116
01110101117
01110110118
01110111119
01111000120
01111001121
01111010122
01111011123
01111100124
01111101125
01111110126
01111111127
10000000128
BinaryDecimal
10000001129
10000010130
10000011131
10000100132
10000101133
10000110134
10000111135
10001000136
10001001137
10001010138
10001011139
10001100140
10001101141
10001110142
10001111143
10010000144
10010001145
10010010146
10010011147
10010100148
10010101149
10010110150
10010111151
10011000152
10011001153
10011010154
10011011155
10011100156
10011101157
10011110158
10011111159
10100000160
10100001161
10100010162
10100011163
10100100164
10100101165
10100110166
10100111167
10101000168
10101001169
10101010170
10101011171
10101100172
10101101173
10101110174
10101111175
10110000176
10110001177
10110010178
10110011179
10110100180
10110101181
10110110182
10110111183
10111000184
10111001185
10111010186
10111011187
10111100188
10111101189
10111110190
10111111191
11000000192
BinaryDecimal
11000001193
11000010194
11000011195
11000100196
11000101197
11000110198
11000111199
11001000200
11001001201
11001010202
11001011203
11001100204
11001101205
11001110206
11001111207
11010000208
11010001209
11010010210
11010011211
11010100212
11010101213
11010110214
11010111215
11011000216
11011001217
11011010218
11011011219
11011100220
11011101221
11011110222
11011111223
11100000224
11100001225
11100010226
11100011227
11100100228
11100101229
11100110230
11100111231
11101000232
11101001233
11101010234
11101011235
11101100236
11101101237
11101110238
11101111239
11110000240
11110001241
11110010242
11110011243
11110100244
11110101245
11110110246
11110111247
11111000248
11111001249
11111010250
11111011251
11111100252
11111101253
11111110254
11111111255

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

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!