# 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.

## 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 (10
^{0}, which equals 1), - 4 is in the position of tens (10
^{1}) - 3 is in the position of hundreds (10
^{2}) - 2 is in the position of thousands (10
^{3}) - 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 * 10
^{3}) + (3 * 10^{2}) + (4 * 10^{1}) + (5 * 10^{0}) + (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 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 2^{0}. 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

Decimal | Binary |
---|---|

1 | 00000001 |

2 | 00000010 |

3 | 00000011 |

4 | 00000100 |

5 | 00000101 |

6 | 00000110 |

7 | 00000111 |

8 | 00001000 |

9 | 00001001 |

10 | 00001010 |

11 | 00001011 |

12 | 00001100 |

13 | 00001101 |

14 | 00001110 |

15 | 00001111 |

16 | 00010000 |

17 | 00010001 |

18 | 00010010 |

19 | 00010011 |

20 | 00010100 |

21 | 00010101 |

22 | 00010110 |

23 | 00010111 |

24 | 00011000 |

25 | 00011001 |

26 | 00011010 |

27 | 00011011 |

28 | 00011100 |

29 | 00011101 |

30 | 00011110 |

31 | 00011111 |

32 | 00100000 |

33 | 00100001 |

34 | 00100010 |

35 | 00100011 |

36 | 00100100 |

37 | 00100101 |

38 | 00100110 |

39 | 00100111 |

40 | 00101000 |

41 | 00101001 |

42 | 00101010 |

43 | 00101011 |

44 | 00101100 |

45 | 00101101 |

46 | 00101110 |

47 | 00101111 |

48 | 00110000 |

49 | 00110001 |

50 | 00110010 |

51 | 00110011 |

52 | 00110100 |

53 | 00110101 |

54 | 00110110 |

55 | 00110111 |

56 | 00111000 |

57 | 00111001 |

58 | 00111010 |

59 | 00111011 |

60 | 00111100 |

61 | 00111101 |

62 | 00111110 |

63 | 00111111 |

64 | 01000000 |

Decimal | Binary |
---|---|

65 | 01000001 |

66 | 01000010 |

67 | 01000011 |

68 | 01000100 |

69 | 01000101 |

70 | 01000110 |

71 | 01000111 |

72 | 01001000 |

73 | 01001001 |

74 | 01001010 |

75 | 01001011 |

76 | 01001100 |

77 | 01001101 |

78 | 01001110 |

79 | 01001111 |

80 | 01010000 |

81 | 01010001 |

82 | 01010010 |

83 | 01010011 |

84 | 01010100 |

85 | 01010101 |

86 | 01010110 |

87 | 01010111 |

88 | 01011000 |

89 | 01011001 |

90 | 01011010 |

91 | 01011011 |

92 | 01011100 |

93 | 01011101 |

94 | 01011110 |

95 | 01011111 |

96 | 01100000 |

97 | 01100001 |

98 | 01100010 |

99 | 01100011 |

100 | 01100100 |

101 | 01100101 |

102 | 01100110 |

103 | 01100111 |

104 | 01101000 |

105 | 01101001 |

106 | 01101010 |

107 | 01101011 |

108 | 01101100 |

109 | 01101101 |

110 | 01101110 |

111 | 01101111 |

112 | 01110000 |

113 | 01110001 |

114 | 01110010 |

115 | 01110011 |

116 | 01110100 |

117 | 01110101 |

118 | 01110110 |

119 | 01110111 |

120 | 01111000 |

121 | 01111001 |

122 | 01111010 |

123 | 01111011 |

124 | 01111100 |

125 | 01111101 |

126 | 01111110 |

127 | 01111111 |

128 | 10000000 |

Decimal | Binary |
---|---|

129 | 10000001 |

130 | 10000010 |

131 | 10000011 |

132 | 10000100 |

133 | 10000101 |

134 | 10000110 |

135 | 10000111 |

136 | 10001000 |

137 | 10001001 |

138 | 10001010 |

139 | 10001011 |

140 | 10001100 |

141 | 10001101 |

142 | 10001110 |

143 | 10001111 |

144 | 10010000 |

145 | 10010001 |

146 | 10010010 |

147 | 10010011 |

148 | 10010100 |

149 | 10010101 |

150 | 10010110 |

151 | 10010111 |

152 | 10011000 |

153 | 10011001 |

154 | 10011010 |

155 | 10011011 |

156 | 10011100 |

157 | 10011101 |

158 | 10011110 |

159 | 10011111 |

160 | 10100000 |

161 | 10100001 |

162 | 10100010 |

163 | 10100011 |

164 | 10100100 |

165 | 10100101 |

166 | 10100110 |

167 | 10100111 |

168 | 10101000 |

169 | 10101001 |

170 | 10101010 |

171 | 10101011 |

172 | 10101100 |

173 | 10101101 |

174 | 10101110 |

175 | 10101111 |

176 | 10110000 |

177 | 10110001 |

178 | 10110010 |

179 | 10110011 |

180 | 10110100 |

181 | 10110101 |

182 | 10110110 |

183 | 10110111 |

184 | 10111000 |

185 | 10111001 |

186 | 10111010 |

187 | 10111011 |

188 | 10111100 |

189 | 10111101 |

190 | 10111110 |

191 | 10111111 |

192 | 11000000 |

Decimal | Binary |
---|---|

193 | 11000001 |

194 | 11000010 |

195 | 11000011 |

196 | 11000100 |

197 | 11000101 |

198 | 11000110 |

199 | 11000111 |

200 | 11001000 |

201 | 11001001 |

202 | 11001010 |

203 | 11001011 |

204 | 11001100 |

205 | 11001101 |

206 | 11001110 |

207 | 11001111 |

208 | 11010000 |

209 | 11010001 |

210 | 11010010 |

211 | 11010011 |

212 | 11010100 |

213 | 11010101 |

214 | 11010110 |

215 | 11010111 |

216 | 11011000 |

217 | 11011001 |

218 | 11011010 |

219 | 11011011 |

220 | 11011100 |

221 | 11011101 |

222 | 11011110 |

223 | 11011111 |

224 | 11100000 |

225 | 11100001 |

226 | 11100010 |

227 | 11100011 |

228 | 11100100 |

229 | 11100101 |

230 | 11100110 |

231 | 11100111 |

232 | 11101000 |

233 | 11101001 |

234 | 11101010 |

235 | 11101011 |

236 | 11101100 |

237 | 11101101 |

238 | 11101110 |

239 | 11101111 |

240 | 11110000 |

241 | 11110001 |

242 | 11110010 |

243 | 11110011 |

244 | 11110100 |

245 | 11110101 |

246 | 11110110 |

247 | 11110111 |

248 | 11111000 |

249 | 11111001 |

250 | 11111010 |

251 | 11111011 |

252 | 11111100 |

253 | 11111101 |

254 | 11111110 |

255 | 11111111 |

## Recent Comments

Amazing

what a understanding

Thanks for giving such information like that

now I can easily convert binary Language

Thanks alot

You can convert decimals too! Woo-hoo! Thanks, Guest!

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PERFECT CONVERSION

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First result on google (search : "dec -> bin")

Quick and easy

Helped me convert my 4 bit pc instruction set

Made my first program : prints 2 to the display lol

22.246 converts to xxx in binary. Break the operation into two parts: Left side of decimal and Right side of decimal. Convert 22 into Binary by dividing by 2 and noting if there is a remainder, if so, write a 1; otherwise write a 0. Read the remainders from bottom to top. To convert the Right side, multiply by 2. Any value > 1, write a 1; otherwise write a 0 and multiply that by 2.

can you explain how to convert 22.246 into decimal

Please work out these method in note book then viewers can understand easily

165.29 decimal to binary conversation

very easy to do and work.

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

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

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