Binary

# Binary To Octal Conversion In binary to octal conversion, we only learn how the base 2 is converted into base 8 number system. The binary to octal conversion is not directly take place. Digital computer can only understand the binary number. At the same time the octal number is also use in electronics computer. In this tutorial we are learn about the binary to octal conversion.
Binary is the simples type of number that use only two digits one is “0” and other is “0” (i.e. value of base 2). The digital electronics only use two states either it is 0 or 1. In modern day computer the binary number use widely. It is also use in communication and other type of professionals.

“Whereas octal number is one of another type of number system. In which have 10 values and it has only 8 symbols that are 0 to 7”.

## What are Binary Numbers?

The binary number system only uses two state that are “0” and “1”.the radix have 2. This number is the primer language of digital computer system. Some example of binary number is (111110)2, (1111111)2, (1011001)2.

## What are Octal numbers?

In octal number system having 8 number which is  0,1,2,3,4,5,6,7. And the radix of this number system is 8. This number was use in ancient of some Native American tribes until 20th century. This number is popular in early age of computing as a language of computer programming. because of shorten of binary number by simplifying long and complex chains of binary displays used by computers.
This number is manly use for binary counting in group forms. The representation of octal number is grouping of three binary bits. Since 8 are 2 to the third power 23.

### Conversion from Binary to Octal number system

The conversion of binary to octal number is easy because octal number has specified value of binary numbers. You just have to remember that each octal value in to three binary bits. You can follow the steps to convert binary to octal number system.

• Step 1: Write down the binary digits and group of three bit. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of three, add extra 0’s to make another group.
• Step 2: Write decimal value 4, 2 and 1 below each group. These are the weights that the positions carry (22, 21, 20).
• Step 3: Every three group of binary bit will give you one digit in octal number.
• Step 4: Add the products.
• Step 5: The sums will give you the octal number; it is from left to right.

Step 1: 111010 has six binary bit and therefore can be grouped in sets of three.
Think of the number as (111)(010).

Step 2: Write decimal value 4,2 and 1 below each binary bit group.

111    010
421    421

Step 3: Multiply the 4, 2 and 1’s with the binary bit above.

111    010
421    421

In the first group, 4 + 2 + 1 = 7
In the second group, 0 + 2 + 0 = 2

111    010
421    421
7      2

Step 5: (111010)2  = (72)8

#### Binary to Octal Conversion Examples

Example 1: (1010001)2 = (121)8
(1)(010)(001)
Here the all bit cannot group all in three. Add two extra bit “0” to from grouping of three bit and repeat the above step.

001     010     001
421     421     421
1        2          1

And result is 121

Example 1: Convert (1010101)2 to octal

Solution:
Given binary number are (1010101)2
First, we convert given binary to decimal
1010101= (1 * 26) + (0 * 2) + (1 * 24) + (0 * 23) + (1 * 22) + (0 * 21) + (1 * 20)
= 64 + 0 + 16 + 0 + 4 + 0 + 1
= 64 + 21
0101012= 85 (Decimal form) Therefore, the equivalent octal number is (125)8.

Example 2: Convert (01101)2 to octal

Solution:
Given binary number are (01101)2
First we convert given binary to decimal
01101= (0 * 24) + (1 * 23) + (1 * 23) + (0 * 2) + (1 *20)
= 0 + 8 + 4 + 0 +1
011012= 13 (Decimal form) Therefore, the equivalent octal number is (15)8.

## Binary Octal Conversion Chart Table

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

#### What is octal equivalent of the binary number 1011 1101?

Binary to Octal conversion table

 Binary Number Octal Number 1010 12 1011 13 1100 14 1101 15

#### What is the octal equivalent of binary number 10111101?

The binary number 10111101 is equivalent to 571
101  111  001
5      7       1

#### What is binary and octal?

The octal and binary number are used to write a number using different rule other than decimal number. In binary number system we only use two binary bit i.e. “0” and “1” but in octal number system we use eight number and that number is 0,1,2,3,4,5,6 and 7.

#### What is the octal equivalent for the binary value of 00001111?

Binary Octal Conversion Chart Table

 Binary Octal 00001110 16 00001111 17 00010000 20 00010001 21

#### What is the octal equivalent of hexadecimal 14?

Octal equivalent of hexadecimal 14 is 1100
Hex to Octal Conversion Table

 Hexadecimal Octal Equivalent Binary B 13 1011 C 14 1100 D 15 1101 E 16 1110

#### What is the binary equivalent of decimal number 12?

binary equivalent of decimal number 12 is 1100
Decimal to Binary Table

 Decimal Number Binary Number 11 1011 12 1100 13 1101 14 1110

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