Decimal to Binary converter

Decimal to binary converter helps you to calculate a binary value from a decimal number. To use this converter, type any decimal value in the first area below. Hit the blue button and then you will see the binary result of the calculation in the second area. You can convert up to to 19 decimal characters to binary (263 − 1) in our converter.




The result of Decimal to Binary conversion in base numbers

Result

Related converters: Binary to Decimal converter, Hex to Decimal converter

Decimal number

A decimal number system is positional numeral system employing 10 as the base. It uses 10 different symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
It is the standard system for denoting integer and non-integer numbers. Decimal number refers to the notation of number in the decimal system (base-10), which contains a decimal separator. In this system the number 423.15 represents the sum ( 4 × 102 ) + ( 2 × 101 ) + ( 3 × 100 ) + ( 1 × 10−1 ) + ( 5 × 10−2 ). Humans mostly use the decimal system. You can convert decimal number to binary with our converter.

Binary number

A binary number is a number which is expressed in the base-2 numeral system. This system is the simplest kind of number system. It uses only two symbols 0 and 1. These can be used to represent all other numbers. The rightmost digit represents one, with each digit to the left doubling in value. Binary numbers can do arithmetic operations. For example addition, subtraction, multiplication or division. It is used by modern computer-based devices and computers because of easy implementation in digital electronic circuitry.

How to convert decimal to binary

Decimal to binary method 1: Positional notation
A positional notation is a numeral system in which each position is related to the next by a constant multiplier, which is called the base or radix. In the binary system, the weight of each digit increases by a factor of 2. The first digit has a weight of 2 0, the second digit has a weight of 2 1 and so on.

The decimal number is equal to the sum: 72308 = 7*10 4 + 2*10 3 + 3*10 2 + 0*10 1 + 8*10 0

 

Decimal to binary method 2: Division by 2
This is an easy method of converting decimal to a binary number. Equivalents to write down the decimal number and to continually divide by 2 to give a result and a remainder of either a 1 or a 0 until the final result is zero. For example convert decimal number 185 to binary looks like:

Division by 2ResultReminderBit position
1859210 (LSB)
92460
1
462302
231113
11514
5215
2106
1017 (MSB)

The result is obtained by placing all the remainders in order, so result of decimal to binary conversion is 10111001.
 

Decimal binary conversion table

In the table below there are decimal to binary conversions for values 0 - 255. You can navigate the table using Previous and Next buttons. You can also sort the table by click on the header.

DecimalBinary
00
11
210
311
4100
5101
6110
7111
81000
91001
101010
111011
121100
131101
141110
151111
1610000
1710001
1810010
1910011
2010100
2110101
2210110
2310111
2411000
2511001
2611010
2711011
2811100
2911101
3011110
3111111
32100000
33100001
34100010
35100011
36100100
37100101
38100110
39100111
40101000
41101001
42101010
43101011
44101100
45101101
46101110
47101111
48110000
49110001
50110010
51110011
52110100
53110101
54110110
55110111
56111000
57111001
58111010
59111011
60111100
61111101
62111110
63111111
641000000
651000001
661000010
671000011
681000100
691000101
701000110
711000111
721001000
731001001
741001010
751001011
761001100
771001101
781001110
791001111
801010000
811010001
821010010
831010011
841010100
851010101
861010110
871010111
881011000
891011001
901011010
911011011
921011100
931011101
941011110
951011111
961100000
971100001
981100010
991100011
1001100100
1011100101
1021100110
1031100111
1041101000
1051101001
1061101010
1071101011
1081101100
1091101101
1101101110
1111101111
1121110000
1131110001
1141110010
1151110011
1161110100
1171110101
1181110110
1191110111
1201111000
1211111001
1221111010
1231111011
1241111100
1251111101
1261111110
1271111111
12810000000
12910000001
13010000010
13110000011
13210000100
13310000101
13410000110
13510000111
13610001000
13710001001
13810001010
13910001011
14010001100
14110001101
14210001110
14310001111
14410010000
14510010001
14610010010
14710010011
14810010100
14910010101
15010010110
15110010111
15210011000
15310011001
15410011010
15510011011
15610011100
15710011101
15810011110
15910011111
16010100000
16110100001
16210100010
16310100011
16410100100
16510100101
16610100110
16710100111
16810101000
16910101001
17010101010
17110101011
17210101100
17310101101
17410101110
17510101111
17610110000
17710110001
17810110010
17910110011
18010110100
18110110101
18210110110
18310110111
18410111000
18510111001
18610111010
18710111011
18810111100
18910111101
19010111110
19110111111
19211000000
19311000001
19411000010
19511000011
19611000100
19711000101
19811000110
19911000111
20011001000
20111001001
20211001010
20311001011
20411001100
20511001101
20611001110
20711001111
20811010000
20911010001
21011010010
21111010011
21211010100
21311010101
21411010110
21511010111
21611011000
21711011001
21811011010
21911011011
22011011100
22111011101
22211011110
22311011111
22411100000
22511100001
22611100010
22711100011
22811100100
22911100101
23011100110
23111100111
23211101000
23311101001
23411101010
23511101011
23611101100
23711101101
23811101110
23911101111
24011110000
24111110001
24211110010
24311110011
24411110100
24511110101
24611110110
24711110111
24811111000
24911111001
25011111010
25111111011
25211111100
25311111101
25411111110
25511111111

Examples of decimal to binary conversions

In the list below there are examples of dec to bin conversions. For the other numbers, you can use our decimal to binary converter tool.

  • Decimal 8 is 1000 in binary.
  • Decimal 31 is 11111 in binary.
  • Decimal 65535 is 1111111111111111 in binary.

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