The number with base eight is called octal number. It is represented by Q or O. We can generate these numbers with the combination of 0, 1, 2 3, 4, 5, 6, 7. We can represent these numbers wit suffix eight. Eg (5432)_{8}
85 | 84 | 83 | 82 | 81 | 80 |
32768 | 4096 | 512 | 64 | 8 | 1 |
Decimal number is repetitively divided by eight and remainders are arranged in the form of octal numbers.
Example
1. Convert (240)_{10}into octal.
8 | 240 | 0 |
8 | 30 | 6 |
3 |
(240)_{10}= (360)_{8}
2. Convert (356)_{10} into octal.
8 | 356 | 4 |
8 | 44 | 4 |
4 |
(365)_{10}=(444)_{8}
Each octal is multiplied by its weighted position. The sum of all products is known as decimal form of octal.
Example
Convert the octal numbers into decimal
The three digit format of binary digits is used for octal to binary conversions or vice-versa.
3-bits binary numbers are written for each octal digit.
Example
Algorithm:
The binary numbers are broken into 3-bits section from last bit and convert into octal equivalent of each binary section. Table shows the decimal, octal and equivalent binary bits.
Decimal | Octal | Binary |
0 | 0 | 000 |
1 | 1 | 001 |
2 | 2 | 010 |
3 | 3 | 011 |
4 | 4 | 100 |
5 | 5 | 101 |
6 | 6 | 110 |
7 | 7 | 111 |
Example
Algorithm
Algorithm
Example
A number system that uses eight different digits to represent different values is known as octal number system. The base of octal number system is 8 because it consist eight digits from 0 to 7. The octal number system is used in the computer to represent binary numbers. The place values in the octal number can be expressed by using powers of 8.
The procedure for conversion of octal numbers to their decimal equivalents is similar to conversion of binary numbers to their decimal equivalents but with the difference, that the base used in this case is 8 instead of 2 used in binary.
Convert (5264)_{8} into Decimal
Solution:
3 2 1 0 (weight)
Octal Number: 5 2 6 4
Decimal Equivalent: 5×8^{3} + 2×8^{2} + 6×8^{1} + 4×8^{0}
= 5×512 + 2×64 + 6×8 + 4×1
= 2560 + 128 + 48 + 4
= 2740
Hence, (5264)_{8 }= (2740)_{10}
Octal digit is represented in 3 bits. An octal number is converted to its binary equivalent by just substituting the respective binary value for each digit of the octal number.
Binary Table
Octal | Binary |
0 | 000 |
1 | 001 |
2 | 010 |
3 | 011 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
Convert (3206)_{8} into Binary
Solution:
Octal Number: 3 2 0 6
Binary Equivalent: 11 010 000 110 (From Binary Table)
Hence, (3206)8 = (11010000110)_{2}
There is no any direct method to convert octal number into octal. So, at first the given octal number is converted into its binary equivalent then the result will be converted into hexadecimal as in previous methods.
Convert (3256)_{8} into Hexadecimal
Octal Number: 3 2 5 6
Binary Equivalent: 11 010 101 110 (From Binary Table)
Again,
Paired Hexadecimal
Equivalent (4 bits): 110 1010 1110 (pairing from right-most digit)
Hexadecimal Equivalent: 6 A E (From Binary Table)
Hence, (3256)_{8} = (6AE)_{16}
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