# Decimal to Binary Converter

To use this decimal to binary converter tool, you should type a decimal value like 308 into the left field below, and then hit the Convert button. This way you can convert up to 19 decimal characters (max. value of 9223372036854775807) to binary value.

swap conversion: Binary To Decimal Converter
Decimal to binary conversion result in base numbers

## 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 Hinduâ€“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)

## 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 signalâ€™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 to binary conversion examples

• (51)10 = (110011)2
• (217)10 = (11011001)2
• (8023)10 = (1111101010111)2

#### Decimal to Binary Conversion Chart Table

DecimalBinary
100000001
200000010
300000011
400000100
500000101
600000110
700000111
800001000
900001001
1000001010
1100001011
1200001100
1300001101
1400001110
1500001111
1600010000
1700010001
1800010010
1900010011
2000010100
2100010101
2200010110
2300010111
2400011000
2500011001
2600011010
2700011011
2800011100
2900011101
3000011110
3100011111
3200100000
3300100001
3400100010
3500100011
3600100100
3700100101
3800100110
3900100111
4000101000
4100101001
4200101010
4300101011
4400101100
4500101101
4600101110
4700101111
4800110000
4900110001
5000110010
5100110011
5200110100
5300110101
5400110110
5500110111
5600111000
5700111001
5800111010
5900111011
6000111100
6100111101
6200111110
6300111111
6401000000
DecimalBinary
6501000001
6601000010
6701000011
6801000100
6901000101
7001000110
7101000111
7201001000
7301001001
7401001010
7501001011
7601001100
7701001101
7801001110
7901001111
8001010000
8101010001
8201010010
8301010011
8401010100
8501010101
8601010110
8701010111
8801011000
8901011001
9001011010
9101011011
9201011100
9301011101
9401011110
9501011111
9601100000
9701100001
9801100010
9901100011
10001100100
10101100101
10201100110
10301100111
10401101000
10501101001
10601101010
10701101011
10801101100
10901101101
11001101110
11101101111
11201110000
11301110001
11401110010
11501110011
11601110100
11701110101
11801110110
11901110111
12001111000
12101111001
12201111010
12301111011
12401111100
12501111101
12601111110
12701111111
12810000000
DecimalBinary
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
DecimalBinary
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

ANONYMOUS i 2021-10-25 14:00:55

Please Explain How Negative number Stored In Binary and Conversion of the Same

Ronan Sally 2021-10-04 10:36:01

This really helped me. I love computers!!! Yay software

Paul 2021-09-30 02:04:10

Write out the table of 2's - 1 2 4 8 16 32 64 128 256
0 1 0 1 0 1 0 0 0
say you want to know what 42 is in binary
start at the table from right to left, so start with 256 column, if 256 is > than 42 then put a 0 in the 256 column, 128 is > 42 so a zero in the 128 column, 64 is > 42 then another zero, 32 < than 42 so you put a 1 in the 42 column, after subtracting 32 from 42 you have 10 left, then go to the next number in the row which is 16, 16 is > 10 so put a 0 in the 16 column, then next number in the row is 8 and 8 can be subtracted from 10 so put a 1 in the 8 column, 10 - 8 leaves 2 left, 4 is > than the remaining 2 left so put a zero in the 4 column, the next number in the row is 2, so 2 - 2 = 0 so put a 1 in the 2 column, since there's nothing left put a 0 in the 1 column... now looking at your chart you can read your binary number from right to left, which is 010101000 which = 42 in binary

Gyana Sahiti 2021-09-23 12:44:46

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David 2021-09-18 22:07:41

Very nice apk make my work easy

bot 2021-09-16 07:32:34

Hansseikha K 2021-09-15 03:12:16

Really helped for a baddie like meh, now I can pass my computer exam

Mysterio 2021-08-19 17:09:47

Quick, Easy and Simple

Zoro 2021-08-15 19:42:56

How to convert fractional decimals to binaries?

Vannuru Pramod 2021-07-12 14:48:51

Helped me cheat in my electrical electronics test

I have always had a problem with Binary. I found it easiest to remember the power of 2 up to a certain number (usually 128 is something I start with), and then you can extrapolate up from there. So what I do to do this freehand, I start with a number I know, let's say you remember 64 is the highest 2 bit operator you remember, so I multiply that until I get over the number I have to convert. So 1024 is too large, so 512 is the first binary number that isn't too large, so you set the bit to 1.
1
Next is 256, and the remainder from subtracting 512 from 789 is 277. You set the bit to 1 to indicate 256.
11
Next is 128, but your remainder is 21. That bit is 0.
110
64, bit is 0.
1100
32, your remainder is 21, so the bit is 0.
11000
16, which is less than 21. So the bit is 1. Remainder is now 5.
110001
8 is the next 2 bit, it's greater than 5 so the bit is 0.
1100010
4, remainder 1. Bit is 1
11000101
2, bit is 0
110001010
1, bit is 1
1100010101
It's tedious, but works. I checked against the calculation on the page, and it's accurate. If you need to put it in bytes, it would be 0011 0001 0101. Each byte is 4 bits, zero padded

DAniel varun 2021-06-15 12:16:54

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Siva 2021-03-29 14:13:31

29.135 decimal to binary

Guest 2021-03-16 14:58:13

Thanks alot
Great effort

Guest 2021-03-09 04:44:45

Cool helped cheat in ICT

Kyiv tor 2021-02-02 23:30:13

What about converting a number such as 125.625

Isuru 2021-01-21 06:18:59

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Dharmik Anghan 2021-01-20 12:33:25

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Moi 2020-12-31 12:47:53

Really good for cheating in my Computer Science test.

Amogh 2020-11-05 16:41:07

keep up the good work