Subject: Computer Science

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}

**Weighted value**

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**

Convert (240)_{10}into octal.

8 | 240 | 0 |

8 | 30 | 6 |

3 |

(240)_{10}= (360)_{8}

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

- (340)
_{8}= 3 x 8^{2}+ 4 x 8^{1}+ 0 x 8^{0}=192 + 32 + 0 = (224)_{10} - (175)
_{8}= 1 x8^{2}+7 x 8^{1}+ 5 x8^{0}= (125)_{10}

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**

Convert (56)_{8} (octal) into binary.

**Algorithm:**

- Convert each octal digit into binary and make three digits grouping.

5= 101

6= 110

Now our equivalent binary number is (56)_{8}=(101110)_{2}

Convert (64102)_{8} into Binary number.

6= 110

4= 100

1= 001

0= 000

2= 010

Now our equivalent binary number is (64102)_{8}= (110100001000010)_{2}

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**

Convert (10011)_{2} into octal number.

**Algorithm**

- make 3-bits grouping from last bit.

010 011 - convert each group into decimal numbers.

010 = 2

011 = 3

= (23)_{8}

Convert (1011010011)_{2} into octal number.

001 011 010 011

001= 1

011= 3

010= 2

011= 3

= (1323)_{8}

**Algorithm**

- Convert octal into binary.
- make groups of 4-bits from last bit.
- convert each group into decimal numbers.

**Example**

1. (34765)_{8}into Hexadecimal number.

- Convert into binary

3= 011, 4= 100, 7=111, 6= 110, 5=101

(011100111110101)_{2} - Make a four digits group from the last bit of the binary number.

0011 1001 1111 0101 (Add 0 before the group to make four digit)

3 9 15 5 (Convert into equivalent decimal numbers)

=(39F5)_{16}Where F= 15

- The number with base eight is called octal number. It is represented by Q or O.
- When decimal number is repetitively divided by eight and remainders are arranged in the form of octal numbers,then decimal number are converted into octal.
- Each octal is multiplied by its weighted position. The sum of all products is known as decimal form of octal.
- The three digit format of binary digits is used for octal to binary conversions or vice versa.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

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.

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 |

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.

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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