Octal system. The base 8 number system is called octal and uses digits 0 to 7. Octal numbers can be constructed from binary numbers by grouping every three consecutive digits of the latter (from right to left) and obtaining their decimal value.
Summary
[ hide ]
- 1 Description
- 2 fractions
- 3 Conversion table between decimal, binary, hexadecimal and octal
- 4 Operations
- 1 Addition
- 2 Multiplication
- 5 Base change
- 1 Decimal to octal basis
- 2 From octal to decimal base
- 6 Sources
Description
The binary number for 74 (in decimal) is 1001010 (in binary), it would be grouped as 1 001 010. So the decimal number 74 in octal is 112. In computing, octal numbering is sometimes used instead of hexadecimal . It has the advantage that it does not require the use of symbols other than digits.
Fractions
Octal numbering is as good as binary and hexadecimal numbering for operating with fractions since the only prime factor for its bases is 2.
| Fraction | Octal | Octal result |
| 1/2 | 1/2 | 0.4 |
| 1/3 | 1/3 | 0.25252525 newspaper |
| 1/4 | 1/4 | 0.2 |
| 1/5 | 1/5 | 0.14631463 newspaper |
| 1/6 | 1/6 | 0.125252525 newspaper |
| 1/7 | 1/7 | 0.111111 newspaper |
| 1/8 | 1/10 | 0.1 |
| 1/9 | 1/11 | 0.07070707 newspaper |
| 1/10 | 1/12 | 0.063146314 newspaper |
Conversion table between decimal, binary, hexadecimal and octal
| Decimal | Binary | Hexadecimal | octal |
| 0 | 00000 | 0 | 0 |
| one | 00001 | one | one |
| 2 | 00010 | 2 | 2 |
| 3 | 00011 | 3 | 3 |
| 4 | 00100 | 4 | 4 |
| 5 | 00101 | 5 | 5 |
| 6 | 00110 | 6 | 6 |
| 7 | 00111 | 7 | 7 |
| 8 | 01000 | 8 | 10 |
| 9 | 01001 | 9 | eleven |
| 10 | 01010 | TO | 12 |
Operations
Addition
| + | 0 | one | 2 | 3 | 4 | 5 | 6 | 7 |
| 0 | 0 | one | 2 | 3 | 4 | 5 | 6 | 7 |
| one | one | 2 | 3 | 4 | 5 | 6 | 7 | 10 |
| 2 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | eleven |
| 3 | 3 | 4 | 5 | 6 | 7 | 10 | eleven | 12 |
| 4 | 4 | 5 | 6 | 7 | 10 | eleven | 12 | 13 |
| 5 | 5 | 6 | 7 | 10 | eleven | 12 | 13 | 14 |
| 6 | 6 | 7 | 10 | eleven | 12 | 13 | 14 | fifteen |
| 7 | 7 | 10 | eleven | 12 | 13 | 14 | fifteen | 16 |
Multiplication
| * | 0 | one | 2 | 3 | 4 | 5 | 6 | 7 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| one | 0 | one | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 0 | 2 | 4 | 6 | 10 | 12 | 14 | 16 |
| 3 | 0 | 3 | 6 | eleven | 14 | 17 | 22 | 25 |
| 4 | 0 | 4 | 10 | 14 | twenty | 24 | 30 | 3. 4 |
| 5 | 0 | 5 | 12 | 17 | 24 | 31 | 36 | 43 |
| 6 | 0 | 6 | 14 | 22 | 30 | 36 | 44 | 52 |
| 7 | 0 | 7 | 16 | 25 | 3. 4 | 43 | 52 | 61 |
Base change
Decimal to octal basis
Let’s see the method to go from the decimal system to the octal system using an example. We will write the number 768 (base 10) in octal base (base 8):
- We divide the number by 8:
- If the quotient is greater than or equal to 8, we divide it by 8.In our case, the quotient is 96 (greater than 8), so we divide it again:
- We continue like this until we get a quotient less than 8.In our case, the quotient is 12 (greater than 8), so we divide it again:
The quotient is 1, less than 8, so we have finished the process. We have indicated the remains with two stripes and the last quotient with a circumference.
- The base 8 number is: (Last quotient) (Last remainder) (Penultimate remainder) … (Second remainder) (First remainder). In our case, the last quotient is 1, the last remainder is 4, the penultimate remainder is 0 and the first remainder is 0. Therefore, the number 768 on an octal basis is 1400.
From octal to decimal base
The method we will follow to pass a number in octal basis to decimal base is:
- From right to left: wemultiply the first number by 1 (1 is 8 raised to 0); the second, by 8 (8 is 8 raised to 1); the third, by 8 raised to 2; the fourth, by 8 raised to 3. And so on until we have multiplied all the figures.
- We addeach of the values obtained.
Example: we pass the number 156 (octal base) to decimal base (base 10):
