Binary

# Convert Octal To Binary | How to Convert Octal To Binary In order to convert octal to binary number system we have some rule. In convert to octal to binary article we are going to discuss about what are the rule we follow and everything. Firstly, what is octal number? The octal number is the part of number system in digital electronics. In digital number there are four type of number that are decimal number, binary number, octal number, hexadecimal number. The octal number have eight number and base is 8, but the binary contain only two number and that number is “0” and “1”. The base of binary is 2.

In convert octal to binary, we convert octal number to decimal number and this decimal number convert to binary equivalent number. We can also remember the octal to binary conversion table so we can quickly convert octal to binary number system. Before we understand conversion method, let us understand about both number systems.

Octal Numbers: The octal number system are that number whose base is 8 and it contains only eight numbers and that number is 0, 1, 2, 3, 4, 5, 6 and 7. These numbers are using to represents the octal number system. . For example:

• 1128
• 10088
• 7898, etc.

Binary Numbers: The binary number systems are that number whose base is 2. The binary number contains only two bits that bits are “0” and “1”. The binary number system is widely use in digital electronics, communication and various thing. Fro storing information in memory we use binary number system. . For example:

• 00112
• 1111012
• 1010102

## How to Convert Octal To Binary?

The conversion of octal to binary number we use two step. First we convert octal number to decimal number and this decimal number is converting into binary number. Let us completely learn step by step here.

### Octal to Decimal Conversion

1. Count the octal number present in the given number. Let the total number is ‘n’.
2. Multiply each octal digit number with 8n-1. The 8n-1 is for nth position from the right end of the number. If the number has a decimal part, multiply each digit in the decimal part by `8-m` when the digit is in the mth position from the decimal point.
3. Add all after multiplication.
4. We obtained the equivalent decimal number.

### Decimal to Binary Conversion

1. The decimal numbers divide it by 2.
2. Note down the remainder.
3. Continue the above two steps till the quotient is zero or one.
4. Write down the remainder in the reverse order.
5. The reverse order is the binary equivalent number of given octal number.

Conversion of octal to binary Conversion of octal to binary in point form #### Solved Examples

Q.1: Convert 418 to a binary number.

Solution: Given octal number is (41)8
(41)8 = [4 * 81] + [1 * 80]
= [4 * 8 ]+ [1 * 1]
= 32+1
= 33(Decimal number)
Now convert this decimal number into binary equivalent number which is given below.

 Decimal Number divided by 2 Quotient Remainder 33 divided by 2 16 1 16 divided by 2 8 0 8 divided by 2 4 0 4 divided by 2 2 0 2 divided by 2 1 0 1 divided by 2 0 1

Therefore, the equivalent binary number is 1000012.
Hence, (41)8 = (100001)2

Q.2: Convert (10)8 to a binary number.

Solution: Given octal number are (10)8
10= [1 * 81] + [0 * 80]
= [1 * 8] + [0 * 1]
= 8 + 0
= 8 (Decimal number)
Now convert this decimal number into binary equivalent number which is given below.

 Decimal Number divided by 2 Quotient Remainder 8 divided by 2 4 0 4 divided by 2 2 0 2 divided by 2 1 0 1 divided by 2 0 1

Therefore, the equivalent binary number is 10002.
Hence, (10)8 = (1000)2

Example: Convert (12)8 into a binary number.

Solution: Given octal number are (12)8.
We take help of binary table, we can write octal number;
128 = (001 010)2
Since zeros is present on the left, we discard the zero because it does not have any significance. Thus,
128 = (1010)2

Practice Questions

1. Convert (122)8into binary number.
2. Convert the octal number (200)8into binary number.
3. Convert (98)8to a binary number.

## Convert Octal to Binary

Converting from octal to binary number has a simple method because octal number is a shortened version of binary string. Always remember the all octal digits represent three binary string of bit. Therefore, one octal number gives three binary bits. While octal number can also be converting by converting into digital and this digital convert into binary. Here a direct method to convert octal to binary is given below in step by step.

• Step 1: Write down the octal number. Each octal digit represents three binary number bits.
• Step 2: Write down the each octal number into binary from in three bits string.
• Step 3: Read 1’s and 0’s you just wrote from left to right. You will get your binary number.

### Some example of octal to binary conversion

Convert the octal number (456)8 into binary number
Step 1:
Octal number =      4           5         6
Binary number = 100          101     110
Step 2:
(456)8 = (1010011100)2

Example 1: (1234)8 = (001010011100) 2

1         2         3         4
001     010     011     100

Example 2: (75426) 8 = (111101100010110) 2

7         5         4         2         6
111     101     100     010     110

Example 3: (6574.73) 8 = (110101111100.111011) 2

6         5         7         4.        7         3
110     101     111     100.    111     011

Binary to Octal Converter

## Convert Octal to Binary Using Table

 Octal Binary Octal Binary Octal Binary Octal Binary 1 00000001 101 01000001 201 10000001 301 11000001 2 00000010 102 01000010 202 10000010 302 11000010 3 00000011 103 01000011 203 10000011 303 11000011 4 00000100 104 01000100 204 10000100 304 11000100 5 00000101 105 01000101 205 10000101 305 11000101 6 00000110 106 01000110 206 10000110 306 11000110 7 00000111 107 01000111 207 10000111 307 11000111 10 00001000 110 01001000 210 10001000 310 11001000 11 00001001 111 01001001 211 10001001 311 11001001 12 00001010 112 01001010 212 10001010 312 11001010 13 00001011 113 01001011 213 10001011 313 11001011 14 00001100 114 01001100 214 10001100 314 11001100 15 00001101 115 01001101 215 10001101 315 11001101 16 00001110 116 01001110 216 10001110 316 11001110 17 00001111 117 01001111 217 10001111 317 11001111 20 00010000 120 01010000 220 10010000 320 11010000 21 00010001 121 01010001 221 10010001 321 11010001 22 00010010 122 01010010 222 10010010 322 11010010 23 00010011 123 01010011 223 10010011 323 11010011 24 00010100 124 01010100 224 10010100 324 11010100 25 00010101 125 01010101 225 10010101 325 11010101 26 00010110 126 01010110 226 10010110 326 11010110 27 00010111 127 01010111 227 10010111 327 11010111 30 00011000 130 01011000 230 10011000 330 11011000 31 00011001 131 01011001 231 10011001 331 11011001 32 00011010 132 01011010 232 10011010 332 11011010 33 00011011 133 01011011 233 10011011 333 11011011 34 00011100 134 01011100 234 10011100 334 11011100 35 00011101 135 01011101 235 10011101 335 11011101 36 00011110 136 01011110 236 10011110 336 11011110 37 00011111 137 01011111 237 10011111 337 11011111 40 00100000 140 01100000 240 10100000 340 11100000 41 00100001 141 01100001 241 10100001 341 11100001 42 00100010 142 01100010 242 10100010 342 11100010 43 00100011 143 01100011 243 10100011 343 11100011 44 00100100 144 01100100 244 10100100 344 11100100 45 00100101 145 01100101 245 10100101 345 11100101 46 00100110 146 01100110 246 10100110 346 11100110 47 00100111 147 01100111 247 10100111 347 11100111 50 00101000 150 01101000 250 10101000 350 11101000 51 00101001 151 01101001 251 10101001 351 11101001 52 00101010 152 01101010 252 10101010 352 11101010 53 00101011 153 01101011 253 10101011 353 11101011 54 00101100 154 01101100 254 10101100 354 11101100 55 00101101 155 01101101 255 10101101 355 11101101 56 00101110 156 01101110 256 10101110 356 11101110 57 00101111 157 01101111 257 10101111 357 11101111 60 00110000 160 01110000 260 10110000 360 11110000 61 00110001 161 01110001 261 10110001 361 11110001 62 00110010 162 01110010 262 10110010 362 11110010 63 00110011 163 01110011 263 10110011 363 11110011 64 00110100 164 01110100 264 10110100 364 11110100 65 00110101 165 01110101 265 10110101 365 11110101 66 00110110 166 01110110 266 10110110 366 11110110 67 00110111 167 01110111 267 10110111 367 11110111 70 00111000 170 01111000 270 10111000 370 11111000 71 00111001 171 01111001 271 10111001 371 11111001 72 00111010 172 01111010 272 10111010 372 11111010 73 00111011 173 01111011 273 10111011 373 11111011 74 00111100 174 01111100 274 10111100 374 11111100 75 00111101 175 01111101 275 10111101 375 11111101 76 00111110 176 01111110 276 10111110 376 11111110 77 00111111 177 01111111 277 10111111 377 11111111 100 01000000 200 10000000 300 11000000

Also read:- Binary to octal conversion.

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