We use the decimal numeral system in our daily life, which is based on 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The binary numeral system, however, is based on 2 numbers: 0 and 1.
To convert a decimal number to binary numeral number, the common way is to keep dividing the number by 2 and write down the remainders from the bottom.
Please check here if you want to convert from a Binary number to a Decimal number.
The following is the example to convert 173 into a binary number:
Step 1: Keep diving 173 by 2, and write down the remainder for each step;
Number | Divided by 2 | Remainder | Check |
---|---|---|---|
173 | 86 | 1 | 86*2+1 =173 |
86 | 43 | 0 | 43*2+0 = 86 |
43 | 21 | 1 | 21*2+1 = 43 |
21 | 10 | 1 | 10*2+1 = 21 |
10 | 5 | 0 | 5*2+0 = 10 |
5 | 2 | 1 | 2*2+1 = 5 |
2 | 1 | 0 | 1*2+0 = 2 |
1 | 0 | 1 | 0*2+1 = 1 |
Step 2: Combine the remainders from the bottom to top. In this example, 73 will be 10101101 when converting into binary.
The following is the Decimal to Binary Conversion Table from 1 to 255
D | Binary | D | Binary | D | Binary | D | Binary |
---|---|---|---|---|---|---|---|
1 | 00000001 | 65 | 01000001 | 129 | 10000001 | 193 | 11000001 |
2 | 00000010 | 66 | 01000010 | 130 | 10000010 | 194 | 11000010 |
3 | 00000011 | 67 | 01000011 | 131 | 10000011 | 195 | 11000011 |
4 | 00000100 | 68 | 01000100 | 132 | 10000100 | 196 | 11000100 |
5 | 00000101 | 69 | 01000101 | 133 | 10000101 | 197 | 11000101 |
6 | 00000110 | 70 | 01000110 | 134 | 10000110 | 198 | 11000110 |
7 | 00000111 | 71 | 01000111 | 135 | 10000111 | 199 | 11000111 |
8 | 00001000 | 72 | 01001000 | 136 | 10001000 | 200 | 11001000 |
9 | 00001001 | 73 | 01001001 | 137 | 10001001 | 201 | 11001001 |
10 | 00001010 | 74 | 01001010 | 138 | 10001010 | 202 | 11001010 |
11 | 00001011 | 75 | 01001011 | 139 | 10001011 | 203 | 11001011 |
12 | 00001100 | 76 | 01001100 | 140 | 10001100 | 204 | 11001100 |
13 | 00001101 | 77 | 01001101 | 141 | 10001101 | 205 | 11001101 |
14 | 00001110 | 78 | 01001110 | 142 | 10001110 | 206 | 11001110 |
15 | 00001111 | 79 | 01001111 | 143 | 10001111 | 207 | 11001111 |
16 | 00010000 | 80 | 01010000 | 144 | 10010000 | 208 | 11010000 |
17 | 00010001 | 81 | 01010001 | 145 | 10010001 | 209 | 11010001 |
18 | 00010010 | 82 | 01010010 | 146 | 10010010 | 210 | 11010010 |
19 | 00010011 | 83 | 01010011 | 147 | 10010011 | 211 | 11010011 |
20 | 00010100 | 84 | 01010100 | 148 | 10010100 | 212 | 11010100 |
21 | 00010101 | 85 | 01010101 | 149 | 10010101 | 213 | 11010101 |
22 | 00010110 | 86 | 01010110 | 150 | 10010110 | 214 | 11010110 |
23 | 00010111 | 87 | 01010111 | 151 | 10010111 | 215 | 11010111 |
24 | 00011000 | 88 | 01011000 | 152 | 10011000 | 216 | 11011000 |
25 | 00011001 | 89 | 01011001 | 153 | 10011001 | 217 | 11011001 |
26 | 00011010 | 90 | 01011010 | 154 | 10011010 | 218 | 11011010 |
27 | 00011011 | 91 | 01011011 | 155 | 10011011 | 219 | 11011011 |
28 | 00011100 | 92 | 01011100 | 156 | 10011100 | 220 | 11011100 |
29 | 00011101 | 93 | 01011101 | 157 | 10011101 | 221 | 11011101 |
30 | 00011110 | 94 | 01011110 | 158 | 10011110 | 222 | 11011110 |
31 | 00011111 | 95 | 01011111 | 159 | 10011111 | 223 | 11011111 |
32 | 00100000 | 96 | 01100000 | 160 | 10100000 | 224 | 11100000 |
33 | 00100001 | 97 | 01100001 | 161 | 10100001 | 225 | 11100001 |
34 | 00100010 | 98 | 01100010 | 162 | 10100010 | 226 | 11100010 |
35 | 00100011 | 99 | 01100011 | 163 | 10100011 | 227 | 11100011 |
36 | 00100100 | 100 | 01100100 | 164 | 10100100 | 228 | 11100100 |
37 | 00100101 | 101 | 01100101 | 165 | 10100101 | 229 | 11100101 |
38 | 00100110 | 102 | 01100110 | 166 | 10100110 | 230 | 11100110 |
39 | 00100111 | 103 | 01100111 | 167 | 10100111 | 231 | 11100111 |
40 | 00101000 | 104 | 01101000 | 168 | 10101000 | 232 | 11101000 |
41 | 00101001 | 105 | 01101001 | 169 | 10101001 | 233 | 11101001 |
42 | 00101010 | 106 | 01101010 | 170 | 10101010 | 234 | 11101010 |
43 | 00101011 | 107 | 01101011 | 171 | 10101011 | 235 | 11101011 |
44 | 00101100 | 108 | 01101100 | 172 | 10101100 | 236 | 11101100 |
45 | 00101101 | 109 | 01101101 | 173 | 10101101 | 237 | 11101101 |
46 | 00101110 | 110 | 01101110 | 174 | 10101110 | 238 | 11101110 |
47 | 00101111 | 111 | 01101111 | 175 | 10101111 | 239 | 11101111 |
48 | 00110000 | 112 | 01110000 | 176 | 10110000 | 240 | 11110000 |
49 | 00110001 | 113 | 01110001 | 177 | 10110001 | 241 | 11110001 |
50 | 00110010 | 114 | 01110010 | 178 | 10110010 | 242 | 11110010 |
51 | 00110011 | 115 | 01110011 | 179 | 10110011 | 243 | 11110011 |
52 | 00110100 | 116 | 01110100 | 180 | 10110100 | 244 | 11110100 |
53 | 00110101 | 117 | 01110101 | 181 | 10110101 | 245 | 11110101 |
54 | 00110110 | 118 | 01110110 | 182 | 10110110 | 246 | 11110110 |
55 | 00110111 | 119 | 01110111 | 183 | 10110111 | 247 | 11110111 |
56 | 00111000 | 120 | 01111000 | 184 | 10111000 | 248 | 11111000 |
57 | 00111001 | 121 | 01111001 | 185 | 10111001 | 249 | 11111001 |
58 | 00111010 | 122 | 01111010 | 186 | 10111010 | 250 | 11111010 |
59 | 00111011 | 123 | 01111011 | 187 | 10111011 | 251 | 11111011 |
60 | 00111100 | 124 | 01111100 | 188 | 10111100 | 252 | 11111100 |
61 | 00111101 | 125 | 01111101 | 189 | 10111101 | 253 | 11111101 |
62 | 00111110 | 126 | 01111110 | 190 | 10111110 | 254 | 11111110 |
63 | 00111111 | 127 | 01111111 | 191 | 10111111 | 255 | 11111111 |
64 | 01000000 | 128 | 10000000 | 192 | 11000000 |